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On de Finetti-type theorems. (English) Zbl 07928320

Ptak, Marek (ed.) et al., Operator and matrix theory, function spaces, and applications. Proceedings of the 33rd international workshop on operator theory and its applications, IWOTA 2022, Kraków, Poland, September 6–10, 2022. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 295, 397-413 (2024).

MSC: 46L53 46L06 60G09 60F20

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Griseta, Maria Elena

On non-commutative spreadability. (English) Zbl 07928308

Ptak, Marek (ed.) et al., Operator and matrix theory, function spaces, and applications. Proceedings of the 33rd international workshop on operator theory and its applications, IWOTA 2022, Kraków, Poland, September 6–10, 2022. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 295, 189-202 (2024).

MSC: 60G09 05A99 16S35 46L53 46L55 46L30

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Wang, Tianhao; Zhong, Xinyi; Fan, Zhou

Universality of approximate message passing algorithms and tensor networks. (English) Zbl 07924322

Ann. Appl. Probab. 34, No. 4, 3943-3994 (2024).

MSC: 94A15 68W40 60B20 15B52

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Chevyrev, Ilya; Ebrahimi-Fard, Kurusch; Patras, Frédéric

Algebraic groups in non-commutative probability theory revisited. (English) Zbl 07923762

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 27, No. 3, Article ID 2450005, 32 p. (2024).

MSC: 16T05 16T10 16T30 17A30 46L53 46L54

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Asai, Nobuhiro; Yoshida, Hiroaki

Combinatorial aspects of weighted free Poisson random variables. (English) Zbl 07923761

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 27, No. 3, Article ID 2450001, 22 p. (2024).

MSC: 46L53 46L54 33D45 60E99 05A30

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Bóna, Miklós (ed.); Bouvel, Mathilde (ed.); Brignall, Robert (ed.); Pantone, Jay (ed.)

Mini-workshop: Permutation patterns. Abstracts from the mini-workshop held January 28 – February 2, 2024. (English) Zbl 07921240

Oberwolfach Rep. 21, No. 1, 273-308 (2024).

MSC: 05-06 00B05 00B25 05A05 05A15 05A16

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Jekel, David; Pi, Jennifer

An elementary proof of the inequality \(\chi \leq \chi^\ast\) for conditional free entropy. (English) Zbl 07921213

Doc. Math. 29, No. 5, 1085-1124 (2024).

MSC: 46L54 46L53 60B20 94A17

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Cho, Ilwoo; Jorgensen, Palle E. T.

Free random variables whose free distributions are dictated by the semicircular law. (English) Zbl 07919752

Adv. Oper. Theory 9, No. 2, Paper No. 34, 39 p. (2024).

MSC: 46L54 47L55

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Leppäjärvi, Leevi; Nechita, Ion; Sengupta, Ritabrata

Generating random Gaussian states. (English) Zbl 07906059

J. Math. Phys. 65, No. 8, Article ID 082201, 21 p. (2024).

MSC: 81P40 81P45 15B52 60B20

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Weigt, Martin

Local nets of unbounded operator algebras. (English) Zbl 07905241

Rev. Math. Phys. 36, No. 7, Article ID 2450013, 26 p. (2024).

MSC: 81T05 46L10 47L60 46N50 81P05 81Q05

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Ejsmont, Wiktor; Hęćka, Patrycja

The Boolean quadratic forms and tangent law. (English) Zbl 07859067

Random Matrices Theory Appl. 13, No. 1, Article ID 2450004, 37 p. (2024).

MSC: 46L54 62E10

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Skoufranis, Paul

Non-commutative stochastic processes and bi-free probability. (English) Zbl 07858215

Indiana Univ. Math. J. 73, No. 2, 421-444 (2024).

Reviewer: Uwe Franz (Besançon)

MSC: 46L53 46L54

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Freslon, Amaury

Advances in quantum permutation groups. (English) Zbl 07840375

Markin, Marat V. (ed.) et al., Advances in functional analysis and operator theory. AMS-EMS-SMF special session, Université de Grenoble-Alpes, Grenoble, France, July 18–22, 2022. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 798, 153-197 (2024).

MSC: 20G42 05E10 05C25 05C10 46L53 46L54

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Arizmendi, Octavio; Cébron, Guillaume; Speicher, Roland; Yin, Sheng

Universality of free random variables: atoms for non-commutative rational functions. (English) Zbl 07829726

Adv. Math. 443, Article ID 109595, 73 p. (2024).

MSC: 47-XX

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Cho, Ilwoo

Free probability on Banach algebras induced by scaled hypercomplex numbers. (English) Zbl 07818527

Complex Anal. Oper. Theory 18, No. 2, Paper No. 27, 52 p. (2024).

MSC: 46S10 46L54 47S10 20G20

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Chétrite, R.; Patras, F.

Algebraic structures underlying quantum independences: theory and applications. (English) Zbl 1540.81005

Ann. Henri Poincaré 25, No. 1, 253-296 (2024).

MSC: 81P05 60A05 46N30 46L53

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Cho, Ilwoo; Dong, Junyi

Catalan numbers and free distributions of mutually free multi semicircular elements. (English) Zbl 07797434

Complex Anal. Oper. Theory 18, No. 2, Paper No. 23, 46 p. (2024).

MSC: 46L54 46L10 11B83 47L55

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Alpay, Daniel; Jorgensen, Palle

Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting. (English) Zbl 07795636

Banach J. Math. Anal. 18, No. 1, Paper No. 5, 24 p. (2024).

MSC: 28A50 60J65 46L53

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Cho, Ilwoo; Jorgensen, Palle E. T.

Free probability on the limit \(C^\ast\)-algebra induced by a chain of graphs. (English) Zbl 1541.46045

Complex Anal. Oper. Theory 18, No. 1, Paper No. 11, 48 p. (2024).

MSC: 46L54 05C20 05C63 17A50 18B40 47A99

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Kabluchko, Zakhar; Marynych, Alexander; Pitters, Helmut

Mod-\( \phi\) convergence of Stirling distributions and limit theorems for zeros of their generating functions. (English) Zbl 1527.60022

J. Math. Anal. Appl. 529, No. 1, Article ID 127571, 27 p. (2024).

Reviewer: Ludwig Paditz (Dresden)

MSC: 60F05 60C05 05A15 11B73

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Speicher, Roland

A short proof for the twisted multiplicativity property of the operator-valued S-transform. (English) Zbl 07918457

Albrecht, Ernst (ed.) et al., Multivariable operator theory. The Jörg Eschmeier memorial volume. Cham: Birkhäuser. 761-768 (2023).

MSC: 46L54

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Venturelli, Davide; Cugliandolo, Leticia F.; Schehr, Grégory; Tarzia, Marco

Replica approach to the generalized Rosenzweig-Porter model. (English) Zbl 07902453

SciPost Phys. 14, No. 5, Paper No. 110, 46 p. (2023).

MSC: 82B10 82B21 82B44 15B52 60B20

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Capitaine, M.; Coste, S.; Gabriel, F.; Maillard, P.; Mailler, C.

Random matrices and random graphs. (English. French summary) Zbl 1536.15035

ESAIM, Proc. Surv. 74, 137-157 (2023).

MSC: 15B52 05C50 05C05 05B45 05B20

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Collins, Benoît

Moment methods on compact groups: Weingarten calculus and its applications. (English) Zbl 07822649

Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 4. Sections 5–8. Berlin: European Mathematical Society (EMS). 3142-3164 (2023).

Reviewer: Yaogan Mensah (Lomé)

MSC: 43A05 15B52 60B20 28C10 46L54 22D20

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Chatzinikolaou, Alexandros

On coproducts of operator \(\mathcal{A}\)-systems. (English) Zbl 07812130

Oper. Matrices 17, No. 2, 435-468 (2023).

MSC: 47L25 46L07 46L09

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Caspers, Martijn

On the isomorphism class of \(q\)-Gaussian \(W^\ast\)-algebras for infinite variables. (English) Zbl 07811833

C. R., Math., Acad. Sci. Paris 361, 1711-1716 (2023).

MSC: 46L10 46L06

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Cho, Ilwoo; Jorgensen, Palle E. T.

On semicircular elements induced by connected finite graphs. (English) Zbl 1534.46057

Moslehian, Mohammad Sal (ed.), Matrix and operator equations and applications. Cham: Springer. Math. Online First Collect., 583-631 (2023).

Reviewer: Hang Lau (Montréal)

MSC: 46L54 22A22 05C99

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Song, Jian; Xiao, Yimin; Yuan, Wangjun

On eigenvalues of the Brownian sheet matrix. (English) Zbl 1531.60011

Stochastic Processes Appl. 166, Article ID 104231, 38 p. (2023).

Reviewer: Yuliya S. Mishura (Kyïv)

MSC: 60B20 60H15 60B10 60G15 60G60

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Au, Benson; Garza-Vargas, Jorge

Spectral asymptotics for contracted tensor ensembles. (English) Zbl 1530.60002

Electron. J. Probab. 28, Paper No. 113, 32 p. (2023).

MSC: 60B20 15B52 46L53 46L54

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Hasebe, Takahiro; Ueda, Yuki

On the free Lévy measure of the normal distribution. (English) Zbl 1542.46049

Electron. J. Probab. 28, Paper No. 133, 19 p. (2023).

MSC: 46L54 30B40 60E07

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Perales, Daniel

On the anti-commutator of two free random variables. (English) Zbl 1541.46047

Indiana Univ. Math. J. 72, No. 5, 1867-1908 (2023).

MSC: 46L54 05A18

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Hoskins, Jeremy; Kabluchko, Zakhar

Dynamics of zeroes under repeated differentiation. (English) Zbl 1539.30002

Exp. Math. 32, No. 4, 573-599 (2023).

Reviewer: Themistocles M. Rassias (Athína)

MSC: 30C15 30B20 60B10

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Alpay, Daniel; Cho, Ilwoo

**Certain invertible operator-block matrices induced by \(C^*\)-algebras and scaled hypercomplex numbers.** (English) Zbl 1535.46052

Res. Math. Sci. 10, No. 4, Paper No. 47, 44 p. (2023).

Reviewer: Huang Wenxue (Scarborough)

MSC: 46G20 46S10 47S10 20G20

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Schlüchtermann, Georg; Wibmer, Michael

Numerical solution of free stochastic differential equations. (English) Zbl 07770180

SIAM J. Numer. Anal. 61, No. 6, 2623-2650 (2023).

MSC: 65C30 46L53 46L54 60H10

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Vazquez-Becerra, Josue

Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles. (English) Zbl 1539.46049

J. Theor. Probab. 36, No. 4, 1972-2039 (2023).

MSC: 46L54 60B20 15B52

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Bikram, Panchugopal; Kumar R., Rahul; Mukherjee, Kunal

Mixed \(q\)-deformed Araki-Woods von Neumann algebras. (English) Zbl 1537.46045

J. Noncommut. Geom. 17, No. 4, 1231-1297 (2023).

MSC: 46L10 46L65 46L40 46L53 46L54 46L36 46C99

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Klep, Igor; Scheiderer, Claus; Volčič, Jurij

Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem. (English) Zbl 1531.13020

Math. Ann. 387, No. 3-4, 1403-1433 (2023).

Reviewer: Lorenzo Baldi (Paris)

MSC: 13J30 46L51 14P99 47A63 47L60

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Oussi, Lahcen

Distribution for non symmetric position operators on the free toy Fock space and its approximation on the full Fock space. (English) Zbl 1529.46046

Complex Anal. Oper. Theory 17, No. 7, Paper No. 117, 20 p. (2023).

Reviewer: Alexander Belton (Plymouth)

MSC: 46L53 46L54 60F05 05A17

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Cho, Ilwoo

Free random variables followed by the semicircular law. (English) Zbl 1536.46055

Complex Anal. Oper. Theory 17, No. 7, Paper No. 116, 45 p. (2023).

MSC: 46L54 46L55

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Brannan, Michael; Gao, Li; Junge, Marius

Complete logarithmic Sobolev inequality via Ricci curvature bounded below. II. (English) Zbl 1535.46070

J. Topol. Anal. 15, No. 3, 741-794 (2023).

Reviewer: Adam Skalski (Warszawa)

MSC: 46L53 47D07 82B10

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Garza-Vargas, Jorge; Kulkarni, Archit

Spectra of infinite graphs via freeness with amalgamation. (English) Zbl 1525.05110

Can. J. Math. 75, No. 5, 1633-1684 (2023).

MSC: 05C50 05C63 05D40 47B36 46L54 58J50 60B15 60G50 60B20

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Chifan, Ionuţ; Ioana, Adrian; Kunnawalkam Elayavalli, Srivatsav

An exotic \(\mathrm{II}_1\) factor without property Gamma. (English) Zbl 1534.46052

Geom. Funct. Anal. 33, No. 5, 1243-1265 (2023).

MSC: 46L36

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Gufler, Stephan; Schertzer, Adrien; Schmidt, Marius A.

On the concavity of the TAP free energy in the SK model. (English) Zbl 1534.82016

Stochastic Processes Appl. 164, 160-182 (2023).

MSC: 82D30 82B44 82C31 60F15 15A18 15B52 60B20

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Tarnowski, Wojciech; Chruściński, Dariusz; Denisov, Sergey; Życzkowski, Karol

Random Lindblad operators obeying detailed balance. (English) Zbl 1531.81128

Open Syst. Inf. Dyn. 30, No. 2, Article ID 2350007, 32 p. (2023).

MSC: 81S22 60J35 60G10 47A10 35P15 15B52 81P16 37H05

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Correa da Silva, Ricardo; Lechner, Gandalf

Modular structure and inclusions of twisted Araki-Woods algebras. (English) Zbl 1531.46040

Commun. Math. Phys. 402, No. 3, 2339-2386 (2023).

MSC: 46L10 46L60 81T05 81R05

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Ding, Xiucai; Ji, Hong Chang

Local laws for multiplication of random matrices. (English) Zbl 1519.60006

Ann. Appl. Probab. 33, No. 4, 2981-3009 (2023).

MSC: 60B20 15B52 46L54

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Collins, Benoît; Lamarre, Pierre Yves Gaudreau; Male, Camille

Asymptotic freeness of unitary matrices in tensor product spaces for invariant states. (English) Zbl 1518.60008

Random Matrices Theory Appl. 12, No. 2, Article ID 2250052, 39 p. (2023).

MSC: 60B20 46L54 60B15

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An, Guimei; Gao, Mingchu

\(R^\ast\)-algebras and \(C^\ast\)-uniqueness of pre-\(C^\ast\)-algebras. (English) Zbl 1528.46040

J. Math. Anal. Appl. 526, No. 2, Article ID 127341, 25 p. (2023).

MSC: 46L05 22D25

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Maejima, Makoto; Sakuma, Noriyoshi

Rates of convergence in the free central limit theorem. (English) Zbl 1527.46040

Stat. Probab. Lett. 197, Article ID 109802, 6 p. (2023).

MSC: 46L54 60F05

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Mai, Tobias; Speicher, Roland; Yin, Sheng

The free field: realization via unbounded operators and Atiyah property. (English) Zbl 1526.46043

J. Funct. Anal. 285, No. 5, Article ID 110016, 50 p. (2023).

MSC: 46L54 12E15

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Alpay, Daniel; Cho, Ilwoo

Operators induced by certain hypercomplex systems. (English) Zbl 1526.46051

Opusc. Math. 43, No. 3, 275-333 (2023).

MSC: 46S10 47S10

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Magee, Michael; Puder, Doron

The asymptotic statistics of random covering surfaces. (English) Zbl 1521.20016

Forum Math. Pi 11, Paper No. e15, 51 p. (2023).

MSC: 20C15 20B30 20P05 20F34 20F65 20F70 60B15 57K20 57M07

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Belinschi, Serban T.; Bercovici, Hari; Ho, Ching-Wei

Regularity for free multiplicative convolution on the unit circle. (English) Zbl 1526.46042

Pac. J. Math. 322, No. 2, 243-250 (2023).

MSC: 46L54 30D05

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Alpay, Daniel; Cho, Ilwoo

Dynamical systems of operators induced by scaled hypercomplex rings. (English) Zbl 1525.46046

Adv. Appl. Clifford Algebr. 33, No. 3, Paper No. 33, 39 p. (2023).

MSC: 46L55 46S10 47S10

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Arizmendi, Octavio; Garza-Vargas, Jorge; Perales, Daniel

Finite free cumulants: multiplicative convolutions, genus expansion and infinitesimal distributions. (English) Zbl 1525.46045

Trans. Am. Math. Soc. 376, No. 6, 4383-4420 (2023).

MSC: 46L54 26C10 60B20

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Gerhold, Malte; Hasebe, Takahiro; Ulrich, Michaël

Towards a classification of multi-faced independence: a representation-theoretic approach. (English) Zbl 1523.46051

J. Funct. Anal. 285, No. 3, Article ID 109907, 66 p. (2023).

Reviewer: Adam Skalski (Warszawa)

MSC: 46L53 46L54 60B99

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Ejsmont, Wiktor

Fock space associated with quadrabasic Hermite orthogonal polynomials. (English) Zbl 1523.46050

Stud. Math. 270, No. 1, 17-56 (2023).

Reviewer: Franco Fagnola (Milano)

MSC: 46L53 47N30 46L54

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Marciniak, Mikołaj

Quadratic coefficients of Goulden-Rattan character polynomials. (English) Zbl 1511.05234

Ann. Comb. 27, No. 1, 109-128 (2023).

MSC: 05E10 05A15 20C30

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Ara, Pere; Buss, Alcides; Costa, Ado Dalla

**Free actions of groups on separated graph \(C^*\)-algebras.** (English) Zbl 1518.46047

Trans. Am. Math. Soc. 376, No. 4, 2875-2919 (2023).

MSC: 46L55

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Crismale, Vitonofrio; Rossi, Stefano

Tail algebras for monotone and \(q\)-deformed exchangeable stochastic processes. (English) Zbl 1518.46044

Ann. Mat. Pura Appl. (4) 202, No. 2, 497-518 (2023).

MSC: 46L53 60F20 60G09 60G10

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Bikram, Panchugopal; Mukherjee, Kunal; Ricard, Éric; Wang, Simeng

On the factoriality of \(q\)-deformed Araki-Woods von Neumann algebras. (English) Zbl 1517.46040

Commun. Math. Phys. 398, No. 2, 797-821 (2023).

MSC: 46L10 46L65

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Arenas Longoria, Iris Stephanie; Mingo, James A.

Freely independent coin tosses, standard Young tableaux, and the Kesten-McKay law. (English) Zbl 1514.46044

Am. Math. Mon. 130, No. 1, 35-48 (2023).

MSC: 46L54 60B20

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Demni, Nizar; Hamdi, Tarek

Relating moments of self-adjoint polynomials in two orthogonal projections. (English) Zbl 1514.46045

Adv. Oper. Theory 8, No. 1, Paper No. 7, 19 p. (2023).

MSC: 46L54 47C15 47B15

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Porat, Motke; Vinnikov, Victor

Realizations of non-commutative rational functions around a matrix centre. II: The lost-abbey conditions. (English) Zbl 1521.16014

Integral Equations Oper. Theory 95, No. 1, Paper No. 1, 58 p. (2023).

Reviewer: Wen-Fong Ke (Tainan)

MSC: 16K40 47A56 93C35 16R50 46L54 90C22

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Cho, Ilwoo; Jorgensen, Palle

Comparing Banach spaces for systems of free random variables followed by the semicircular law. (English) Zbl 07678118

Aron, Richard M. (ed.) et al., Operator and norm inequalities and related topics. Cham: Birkhäuser. Trends Math., 773-822 (2022).

MSC: 46L54

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Belinschi, Serban; Guionnet, Alice; Huang, Jiaoyang

Large deviation principles via spherical integrals. (English) Zbl 1511.60047

Probab. Math. Phys. 3, No. 3, 543-625 (2022).

Reviewer: Yuliya S. Mishura (Kyïv)

MSC: 60F10 05E05 60B20

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Collins, Benoît; Parraud, Félix

Concentration estimates for random subspaces of a tensor product and application to quantum information theory. (English) Zbl 1507.81055

J. Math. Phys. 63, No. 10, Article ID 102202, 13 p. (2022).

MSC: 81P45 81P16 94A40 46L54 15B52 60B15

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Lenczewski, Romuald

Motzkin path decompositions of functionals in noncommutative probability. (English) Zbl 1516.46043

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 4, Article ID 2240002, 44 p. (2022).

MSC: 46L53 46L54

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Shlyakhtenko, Dimitri; Tao, Terence

Fractional free convolution powers. (English) Zbl 1518.46046

Indiana Univ. Math. J. 71, No. 6, 2551-2594 (2022).

MSC: 46L54 60B20 15B52

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Backlinks: MO

Popa, Gabriela; Stan, Aurel I.

Quantum operators of the semicircle distributions. (English) Zbl 1512.46044

Accardi, Luigi (ed.) et al., Infinite dimensional analysis, quantum probability and applications, QP41. Proceedings of the 41st conference, United Arab Emirates University (UAEU), Al Ain, Abu Dhabi, United Arab Emirates, virtual, March 28 – April 1, 2021. Cham: Springer. Springer Proc. Math. Stat. 390, 73-88 (2022).

MSC: 46L53

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Ebrahimi-Fard, Kurusch; Patras, Frédéric; Tapia, Nikolas; Zambotti, Lorenzo

Wick polynomials in noncommutative probability: a group-theoretical approach. (English) Zbl 1506.17002

Can. J. Math. 74, No. 6, 1673-1699 (2022).

Reviewer: Loïc Foissy (Calais)

MSC: 17A30 46L53 46L54 16T05 16T10 16T30

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Au, Benson

Semicircular families of general covariance from Wigner matrices with permuted entries. (English) Zbl 1501.60002

Probab. Theory Relat. Fields 184, No. 3-4, 1167-1196 (2022).

MSC: 60B20 46L54 46L53 15B52

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Gangbo, Wilfrid; Jekel, David; Nam, Kyeongsik; Shlyakhtenko, Dimitri

Duality for optimal couplings in free probability. (English) Zbl 1510.46041

Commun. Math. Phys. 396, No. 3, 903-981 (2022).

MSC: 46L54 46L53

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Ball, Joseph A.; Bolotnikov, Vladimir

The rational interpolation problem: Grassmannian and Loewner-matrix approaches. (English) Zbl 1508.30073

Beattie, Christopher (ed.) et al., Realization and model reduction of dynamical systems. A festschrift in honor of the 70th birthday of Thanos Antoulas. Cham: Springer. 3-21 (2022).

MSC: 30E05 47A57 41A05

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Choi, B. J.; Ji, U. C.; Shin, D.

Precise asymptotics of weighted sequences and their applications. (English) Zbl 1524.60065

Acta Math. Hung. 167, No. 1, 161-179 (2022).

MSC: 60F15 46L53

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Alekseev, Vadim; Thom, Andreas

Maximal discrete subgroups in unitary groups of operator algebras. (English) Zbl 1503.46048

SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 052, 7 p. (2022).

MSC: 46L10 22E40 20F38

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Miyagawa, Akihiro

A characterization of rationality in free semicircular operators. (English) Zbl 1500.81050

J. Funct. Anal. 283, No. 8, Article ID 109609, 24 p. (2022).

MSC: 81R60 20E06 30H20 81S05 81Q12

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Kiselev, Alexander; Tan, Changhui

The flow of polynomial roots under differentiation. (English) Zbl 1495.35177

Ann. PDE 8, No. 2, Paper No. 16, 69 p. (2022).

MSC: 35R09 26C10 35Q49 35Q70 44A15 46L54 60B20

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Mingo, James A.; Popa, Mihai; Szpojankowski, Kamil

On the partial transpose of a Haar unitary matrix. (English) Zbl 1504.60015

Stud. Math. 266, No. 3, 337-359 (2022).

Reviewer: Göran Högnäs (Åbo)

MSC: 60B20 46L54 46L53

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Hayes, Ben

A random matrix approach to the Peterson-Thom conjecture. (English) Zbl 1503.46049

Indiana Univ. Math. J. 71, No. 3, 1243-1297 (2022).

MSC: 46L10 46L36 60B20

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Jekel, David; Li, Wuchen; Shlyakhtenko, Dimitri

Tracial smooth functions of non-commuting variables and the free Wasserstein manifold. (English) Zbl 1502.46052

Diss. Math. 580, 1-150 (2022).

MSC: 46L54 46L52 35Q49 94A17 58D99

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Speicher, Roland

A short proof for the twisted multiplicativity property of the operator-valued \(S\)-transform. (English) Zbl 1502.46054

Complex Anal. Oper. Theory 16, No. 6, Paper No. 81, 8 p. (2022).

MSC: 46L54

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OA License

Endo, Taiki; Katori, Makoto; Sakuma, Noriyoshi

Functional equations solving initial-value problems of complex Burgers-type equations for one-dimensional log-gases. (English) Zbl 1492.82010

SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 049, 22 p. (2022).

MSC: 82C22 60B20 44A15 46L54

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Bertucci, Charles; Debbah, Mérouane; Lasry, Jean-Michel; Lions, Pierre-Louis

A spectral dominance approach to large random matrices. (English. French summary) Zbl 1492.60013

J. Math. Pures Appl. (9) 164, 27-56 (2022).

MSC: 60B20 35D40 60F99

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Klep, Igor; Magron, Victor; Povh, Janez

Sparse noncommutative polynomial optimization. (English) Zbl 1494.90072

Math. Program. 193, No. 2 (B), 789-829 (2022).

MSC: 90C23 90C22 47N10 13J10

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Szabłowski, Paweł J.

On the families of polynomials forming a part of the Askey-Wilson scheme and their probabilistic applications. (English) Zbl 1509.33020

Infin. Dimens. Anal. Quantum Probab. Relat. Top. 25, No. 1, Article ID 2230001, 57 p. (2022).

MSC: 33D45 05A30 42C05 60E05

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Isono, Yusuke

Unitary conjugacy for type III subfactors and \(W^\ast\)-superrigidity. (English) Zbl 1496.46056

J. Eur. Math. Soc. (JEMS) 24, No. 5, 1679-1721 (2022).

Reviewer: Sven Raum (Stockholm)

MSC: 46L10 46L36 46L55 37A20

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Jury, Michael T.; Martin, Robert T. W.

Fatou’s theorem for non-commutative measures. (English) Zbl 1505.46052

Adv. Math. 400, Article ID 108293, 53 p. (2022).

MSC: 46L51 47A13

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Zhou, Cong

Limit laws for \(R\)-diagonal variables in a tracial probability space. (English) Zbl 1496.46065

Integral Equations Oper. Theory 94, No. 1, Paper No. 9, 14 p. (2022).

MSC: 46L53 60E07 60E10

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Hall, Brian C.; Ho, Ching-Wei

The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element. (English) Zbl 1491.60014

Lett. Math. Phys. 112, No. 2, Paper No. 19, 61 p. (2022).

MSC: 60B20 46L54

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Chistyakov, G. P.; Götze, F.

Approximation of free convolutions by free infinitely divisible laws. (English) Zbl 07481231

Theory Probab. Appl. 66, No. 4, 640-667 (2022); and Teor. Veroyatn. Primen. 66, No. 4, 806-838 (2021).

Reviewer: Vakhtang V. Kvaratskhelia (Tbilisi)

MSC: 60B05 60B10 60E07

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Song, Jian; Yao, Jianfeng; Yuan, Wangjun

Recent advances on eigenvalues of matrix-valued stochastic processes. (English) Zbl 1480.60056

J. Multivariate Anal. 188, Article ID 104847, 24 p. (2022).

Reviewer: Anatoliy Swishchuk (Calgary)

MSC: 60F05 60G22 15A18 62H10 60H15

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Zhou, Cong

Hinčin’s theorem for additive free convolutions of tracial \(R\)-diagonal \(\ast\)-distributions. (English) Zbl 1492.46061

Complex Anal. Oper. Theory 16, No. 1, Paper No. 1, 9 p. (2022).

MSC: 46L54 60E07

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Cho, Ilwoo

**Group dynamical systems on \(C^*\)-algebras generated by countable infinitely many semicircular elements.** (English) Zbl 1483.46066

Singh, Jagdev (ed.) et al., Methods of mathematical modelling and computation for complex systems. Cham: Springer. Stud. Syst. Decis. Control 373, 159-205 (2022).

MSC: 46L54 46L55

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Fakhri, H.; Refahinozhat, M.

Coherent states attached to the quantum disc algebra and their associated polynomials. (English) Zbl 07830902

Int. J. Geom. Methods Mod. Phys. 18, No. 5, Article ID 2150078, 16 p. (2021).

MSC: 17B37 81R30 05A30 33D45

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Lehner, Franz; Szpojankowski, Kamil

Boolean cumulants and subordination in free probability. (English) Zbl 1537.46053

Random Matrices Theory Appl. 10, No. 4, Article ID 2150036, 46 p. (2021).

MSC: 46L54 60B20

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Cho, Ilwoo; Jorgensen, Palle E. T.

Multi variable semicircular processes from \(\ast\)-homomorphisms and operators. (English) Zbl 1510.46040

Alpay, Daniel (ed.) et al., New directions in function theory: from complex to hypercomplex to non-commutative. Selected papers based on the presentations at the conference, Chapman University, Orange, CA, USA, November 21–26, 2019. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 286, 199-242 (2021).

MSC: 46L54 46L10 46L40 46L53 47L15 47L30 47L55

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Gao, Li; Harris, Samuel J.; Junge, Marius

Quantum teleportation and super-dense coding in operator algebras. (English) Zbl 1490.81042

Int. Math. Res. Not. 2021, No. 12, 9146-9179 (2021).

MSC: 81P45 81P40 46L10 16E40

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González-Pérez, Adrían Manuel; Junge, Marius; Parcet, Javier

Singular integrals in quantum Euclidean spaces. (English) Zbl 1495.42001

Memoirs of the American Mathematical Society 1334. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-4937-7/pbk; 978-1-4704-6750-0/ebook). v, 90 p. (2021).

Reviewer: Sibei Yang (Lanzhou)

MSC: 42-02 42B20 42B37 47G30 46L51 46L10 81R60

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Cho, Ilwoo

Spectral properties of certain operators on the free Hilbert space \(\mathfrak{F}[H_1,\ldots,H_N]\) and the semicircular law. (English) Zbl 1493.46077

Opusc. Math. 41, No. 6, 755-803 (2021).

MSC: 46L10 46L54 47L30 47L55 47B02

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Found 614 Documents (Results 1–100)

On de Finetti-type theorems. (English) Zbl 07928320

On non-commutative spreadability. (English) Zbl 07928308

Universality of approximate message passing algorithms and tensor networks. (English) Zbl 07924322

Algebraic groups in non-commutative probability theory revisited. (English) Zbl 07923762

Combinatorial aspects of weighted free Poisson random variables. (English) Zbl 07923761

Mini-workshop: Permutation patterns. Abstracts from the mini-workshop held January 28 – February 2, 2024. (English) Zbl 07921240

An elementary proof of the inequality \(\chi \leq \chi^\ast\) for conditional free entropy. (English) Zbl 07921213

Free random variables whose free distributions are dictated by the semicircular law. (English) Zbl 07919752

Generating random Gaussian states. (English) Zbl 07906059

Local nets of unbounded operator algebras. (English) Zbl 07905241

The Boolean quadratic forms and tangent law. (English) Zbl 07859067

Non-commutative stochastic processes and bi-free probability. (English) Zbl 07858215

Advances in quantum permutation groups. (English) Zbl 07840375

Universality of free random variables: atoms for non-commutative rational functions. (English) Zbl 07829726

Free probability on Banach algebras induced by scaled hypercomplex numbers. (English) Zbl 07818527

Algebraic structures underlying quantum independences: theory and applications. (English) Zbl 1540.81005

Catalan numbers and free distributions of mutually free multi semicircular elements. (English) Zbl 07797434

Transfer operators and conditional expectations: the non-commutative case, the case of mu-Brownian motions and white noise space setting. (English) Zbl 07795636

Free probability on the limit \(C^\ast\)-algebra induced by a chain of graphs. (English) Zbl 1541.46045

Mod-\( \phi\) convergence of Stirling distributions and limit theorems for zeros of their generating functions. (English) Zbl 1527.60022

A short proof for the twisted multiplicativity property of the operator-valued S-transform. (English) Zbl 07918457

Replica approach to the generalized Rosenzweig-Porter model. (English) Zbl 07902453

Random matrices and random graphs. (English. French summary) Zbl 1536.15035

Moment methods on compact groups: Weingarten calculus and its applications. (English) Zbl 07822649

On coproducts of operator \(\mathcal{A}\)-systems. (English) Zbl 07812130

On the isomorphism class of \(q\)-Gaussian \(W^\ast\)-algebras for infinite variables. (English) Zbl 07811833

On semicircular elements induced by connected finite graphs. (English) Zbl 1534.46057

On eigenvalues of the Brownian sheet matrix. (English) Zbl 1531.60011

Spectral asymptotics for contracted tensor ensembles. (English) Zbl 1530.60002

On the free Lévy measure of the normal distribution. (English) Zbl 1542.46049

On the anti-commutator of two free random variables. (English) Zbl 1541.46047

Dynamics of zeroes under repeated differentiation. (English) Zbl 1539.30002

Certain invertible operator-block matrices induced by \(C^*\)-algebras and scaled hypercomplex numbers. (English) Zbl 1535.46052

Numerical solution of free stochastic differential equations. (English) Zbl 07770180

Fluctuation moments induced by conjugation with asymptotically liberating random matrix ensembles. (English) Zbl 1539.46049

Mixed \(q\)-deformed Araki-Woods von Neumann algebras. (English) Zbl 1537.46045

Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem. (English) Zbl 1531.13020

Distribution for non symmetric position operators on the free toy Fock space and its approximation on the full Fock space. (English) Zbl 1529.46046

Free random variables followed by the semicircular law. (English) Zbl 1536.46055

Complete logarithmic Sobolev inequality via Ricci curvature bounded below. II. (English) Zbl 1535.46070

Spectra of infinite graphs via freeness with amalgamation. (English) Zbl 1525.05110

An exotic \(\mathrm{II}_1\) factor without property Gamma. (English) Zbl 1534.46052

On the concavity of the TAP free energy in the SK model. (English) Zbl 1534.82016

Random Lindblad operators obeying detailed balance. (English) Zbl 1531.81128

Modular structure and inclusions of twisted Araki-Woods algebras. (English) Zbl 1531.46040

Local laws for multiplication of random matrices. (English) Zbl 1519.60006

Asymptotic freeness of unitary matrices in tensor product spaces for invariant states. (English) Zbl 1518.60008

\(R^\ast\)-algebras and \(C^\ast\)-uniqueness of pre-\(C^\ast\)-algebras. (English) Zbl 1528.46040

Rates of convergence in the free central limit theorem. (English) Zbl 1527.46040

The free field: realization via unbounded operators and Atiyah property. (English) Zbl 1526.46043

Operators induced by certain hypercomplex systems. (English) Zbl 1526.46051

The asymptotic statistics of random covering surfaces. (English) Zbl 1521.20016

Regularity for free multiplicative convolution on the unit circle. (English) Zbl 1526.46042

Dynamical systems of operators induced by scaled hypercomplex rings. (English) Zbl 1525.46046

Finite free cumulants: multiplicative convolutions, genus expansion and infinitesimal distributions. (English) Zbl 1525.46045

Towards a classification of multi-faced independence: a representation-theoretic approach. (English) Zbl 1523.46051

Fock space associated with quadrabasic Hermite orthogonal polynomials. (English) Zbl 1523.46050

Quadratic coefficients of Goulden-Rattan character polynomials. (English) Zbl 1511.05234

Free actions of groups on separated graph \(C^*\)-algebras. (English) Zbl 1518.46047

Tail algebras for monotone and \(q\)-deformed exchangeable stochastic processes. (English) Zbl 1518.46044

On the factoriality of \(q\)-deformed Araki-Woods von Neumann algebras. (English) Zbl 1517.46040

Freely independent coin tosses, standard Young tableaux, and the Kesten-McKay law. (English) Zbl 1514.46044

Relating moments of self-adjoint polynomials in two orthogonal projections. (English) Zbl 1514.46045

Realizations of non-commutative rational functions around a matrix centre. II: The lost-abbey conditions. (English) Zbl 1521.16014

Comparing Banach spaces for systems of free random variables followed by the semicircular law. (English) Zbl 07678118

Large deviation principles via spherical integrals. (English) Zbl 1511.60047

Concentration estimates for random subspaces of a tensor product and application to quantum information theory. (English) Zbl 1507.81055

Motzkin path decompositions of functionals in noncommutative probability. (English) Zbl 1516.46043

Fractional free convolution powers. (English) Zbl 1518.46046

Quantum operators of the semicircle distributions. (English) Zbl 1512.46044

Wick polynomials in noncommutative probability: a group-theoretical approach. (English) Zbl 1506.17002

Semicircular families of general covariance from Wigner matrices with permuted entries. (English) Zbl 1501.60002

Duality for optimal couplings in free probability. (English) Zbl 1510.46041

The rational interpolation problem: Grassmannian and Loewner-matrix approaches. (English) Zbl 1508.30073

**Certain invertible operator-block matrices induced by \(C^*\)-algebras and scaled hypercomplex numbers.** (English) Zbl 1535.46052

**Free actions of groups on separated graph \(C^*\)-algebras.** (English) Zbl 1518.46047