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Nonlinear Fokker-Planck flows and their probabilistic counterparts. (English) Zbl 07863722

Lecture Notes in Mathematics 2353. Cham: Springer (ISBN 978-3-031-61733-1/pbk; 978-3-031-61734-8/ebook). ix, 212 p. (2024).

Reviewer: Alain Brillard (Riedisheim)

MSC: 35Q84 35-02 35Q83 35R60 60J25 60J60 35D30 35B40 35B41 35B65 35A01 35A02 37L05 82D30

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Ramanan, Kavita

Interacting stochastic processes on sparse random graphs. (English) Zbl 1533.60181

Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 6. Sections 12–14. Berlin: European Mathematical Society (EMS). 4394-4425 (2023).

MSC: 60K35 60G60 60J60 60J27 60J80 60F15

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Rutten, Daan; Mukherjee, Debankur

Load balancing under strict compatibility constraints. (English) Zbl 1532.60197

Math. Oper. Res. 48, No. 1, 227-256 (2023).

MSC: 60K25 60F17 60J27 60G55 68M20

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Ma, Xiao; Qi, Qingyuan; Li, Xun; Zhang, Huanshui

Optimal control and stabilization for linear continuous-time mean-field systems with delay. (English) Zbl 07903449

IET Control Theory Appl. 16, No. 3, 283-300 (2022).

MSC: 49K10

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Nguyen, Son L.; Yin, George; Nguyen, Dung T.

A general stochastic maximum principle for mean-field controls with regime switching. (English) Zbl 1475.60140

Appl. Math. Optim. 84, No. 3, 3255-3294 (2021).

MSC: 60J25 60J27 60J60 93E20 37N35 37N40

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Dai Pra, Paolo; Formentin, Marco; Pelino, Guglielmo

A hierarchical mean field model of interacting spins. (English) Zbl 1471.58037

Stochastic Processes Appl. 140, 287-338 (2021).

MSC: 58J65 60J25 60J60 60K35 82C22 82C44

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Diez, Antoine

Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles. (English) Zbl 1448.35507

Electron. J. Probab. 25, Paper No. 90, 38 p. (2020).

MSC: 35Q82 35Q83 60J76 60J25 60K35 82C22

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Mach, Tibor; Sturm, Anja; Swart, Jan M.

Recursive tree processes and the mean-field limit of stochastic flows. (English) Zbl 1446.82054

Electron. J. Probab. 25, Paper No. 61, 63 p. (2020).

MSC: 82C22 60J25 60J80 60K35

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Sun, Wen; Philippe, Robert

Analysis of large urn models with local mean-field interactions. (English) Zbl 1412.60113

Electron. J. Probab. 24, Paper No. 45, 33 p. (2019).

MSC: 60J27 60K25 68M15

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Daus, Esther S.; Desvillettes, Laurent; Dietert, Helge

About the entropic structure of detailed balanced multi-species cross-diffusion equations. (English) Zbl 1405.35082

J. Differ. Equations 266, No. 7, 3861-3882 (2019).

Reviewer: E. Ahmed (Mansoura)

MSC: 35K55 35K57 35Q92 60J28 82C22 92D25

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Ma, Limin; Li, Yan; Zhang, Tianliang

Characterization of stochastic mean-field type \(\mathcal{H}\_\) index. (English) Zbl 1407.93356

Asian J. Control 20, No. 5, 1917-1927 (2018).

MSC: 93E03 93C15 60H10

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Simon, Péter L.; Kiss, Istvan Z.

On bounding exact models of epidemic spread on networks. (English) Zbl 1398.34067

Discrete Contin. Dyn. Syst., Ser. B 23, No. 5, 2005-2020 (2018).

MSC: 34C60 34C23 92D30 34C12 60J28 92B20 34A40

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Aghajani, Reza; Robert, Philippe; Sun, Wen

A large scale analysis of unreliable stochastic networks. (English) Zbl 1391.60219

Ann. Appl. Probab. 28, No. 2, 851-887 (2018).

MSC: 60K10 60J27 60K25 68M15

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Collet, Francesca; Kraaij, Richard C.

Path-space moderate deviation principles for the random field Curie-Weiss model. (English) Zbl 1390.60102

Electron. J. Probab. 23, Paper No. 21, 45 p. (2018).

MSC: 60F10 60J27 60K35 82C44

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Karthik, A.; Mukhopadhyay, Arpan; Mazumdar, Ravi R.

Choosing among heterogeneous server clouds. (English) Zbl 1368.60100

Queueing Syst. 85, No. 1-2, 1-29 (2017).

MSC: 60K35 60J27 60J28 90B15 68M20

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Landim, C.; Seo, I.

Metastability of non-reversible, mean-field Potts model with three spins. (English) Zbl 1360.82055

J. Stat. Phys. 165, No. 4, 693-726 (2016).

MSC: 82B20 60J27

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Galves, Antonio; Löcherbach, Eva

Modeling networks of spiking neurons as interacting processes with memory of variable length. (Modéliser les décharges de neurones par des processus en interactions avec une mémoire de longueur variable.) (English. French summary) Zbl 1357.92012

J. SFdS 157, No. 1, 17-32 (2016).

MSC: 92C20 60K35 60G55 60J25 60J55

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Fournier, Nicolas; Löcherbach, Eva

On a toy model of interacting neurons. (English. French summary) Zbl 1355.92014

Ann. Inst. Henri Poincaré, Probab. Stat. 52, No. 4, 1844-1876 (2016).

MSC: 92C20 60K35 60J25 60H10 60G55 60F17

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Erbar, Matthias; Fathi, Max; Laschos, Vaios; Schlichting, André

Gradient flow structure for McKean-Vlasov equations on discrete spaces. (English) Zbl 1353.60084

Discrete Contin. Dyn. Syst. 36, No. 12, 6799-6833 (2016).

MSC: 60K35 60J27 34A34 49J45

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Bortolussi, Luca; Gast, Nicolas

Mean-field limits beyond ordinary differential equations. (English) Zbl 1346.68217

Bernardo, Marco (ed.) et al., Formal methods for the quantitative evaluation of collective adaptive systems. 16th international school on formal methods for the design of computer, communication, and software systems, SFM 2016, Bertinoro, Italy, June 20–24, 2016. Advanced lectures. Cham: Springer (ISBN 978-3-319-34095-1/pbk; 978-3-319-34096-8/ebook). Lecture Notes in Computer Science 9700, 61-82 (2016).

MSC: 68T42 34A60 34F05 60J28 68Q45 68Q87

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Bortolussi, Luca

Hybrid behaviour of Markov population models. (English) Zbl 1336.68177

Inf. Comput. 247, 37-86 (2016).

MSC: 68Q85 60J25 60J28 68Q87 92D25

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Ma, Limin; Zhang, Tianliang; Zhang, Weihai; Chen, Bor-Sen

Finite horizon mean-field stochastic \(H_2/H_\infty\) control for continuous-time systems with \((x,v)\)-dependent noise. (English) Zbl 1395.93578

J. Franklin Inst. 352, No. 12, 5393-5414 (2015).

MSC: 93E20 93E03 49N10 60H10

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Horváth, Kristóf Attila; Telek, Miklós

Task delegation in a peer-to-peer volunteer computing platform. (English) Zbl 1392.68098

Gribaudo, Marco (ed.) et al., Analytical and stochastic modelling techniques and applications. 22nd international conference, ASMTA 2015, Albena, Bulgaria, May 26–29, 2015. Proceedings. Cham: Springer (ISBN 978-3-319-18578-1/pbk; 978-3-319-18579-8/ebook). Lecture Notes in Computer Science 9081, 115-129 (2015).

MSC: 68M14 60J28 68Q87

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Budhiraja, Amarjit; Dupuis, Paul; Fischer, Markus; Ramanan, Kavita

Limits of relative entropies associated with weakly interacting particle systems. (English) Zbl 1321.60202

Electron. J. Probab. 20, Paper No. 80, 22 p. (2015).

MSC: 60K35 60J27 60F10 93D30 34D20

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Miękisz, Jacek; Szymańska, Paulina

On spins and genes. (English) Zbl 1320.00038

Math. Appl. (Warsaw) 40, No. 1, 15-25 (2012).

MSC: 00A71 60J28 68U10 82C20 92D10 92D25

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Bátkai, András; Kiss, Istvan Z.; Sikolya, Eszter; Simon, Péter L.

Differential equation approximations of stochastic network processes: an operator semigroup approach. (English) Zbl 1483.47125

Netw. Heterog. Media 7, No. 1, 43-58 (2012).

MSC: 47N30 60J27 34A34 47D07 60J28

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Koga, Akihisa; Werner, Philipp

Pseudogap behavior in the infinite dimensional attractive Hubbard model. (English) Zbl 1259.82059

Mod. Phys. Lett. B 25, No. 12-13, 973-978 (2011).

MSC: 82C20 82C80 82D50 82C27

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Cohn, Ido; El-Hay, Tal; Friedman, Nir; Kupferman, Raz

Mean field variational approximation for continuous-time Bayesian networks. (English) Zbl 1242.68215

J. Mach. Learn. Res. 11, 2745-2783 (2010).

MSC: 68T05 62F15 60J25

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Rybko, Alexander; Shlosman, Senya

Phase transitions in the queuing networks and the violation of the Poisson hypothesis. (English) Zbl 1155.82012

Mosc. Math. J. 8, No. 1, 159-180 (2008).

MSC: 82C20 60J25 82C26

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McDonald, D. R.; Reynier, J.

Mean field convergence of a model of multiple TCP connections through a buffer implementing RED. (English) Zbl 1094.60053

Ann. Appl. Probab. 16, No. 1, 244-294 (2006).

Reviewer: P. R. Parthasarathy (Chennai)

MSC: 60J25 60K35 94C99

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Rybko, Alexander; Shlosman, Senya

Poisson hypothesis for information networks. I. (English) Zbl 1111.82034

Mosc. Math. J. 5, No. 3, 679-704 (2005).

MSC: 82C20 60J25

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Kurita, Naoki; Funahashi, Ken-ichi

On the Hopfield neural networks and mean field theory. (English) Zbl 0869.68080

Neural Netw. 9, No. 9, 1531-1540 (1996).

MSC: 68T05

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Found 32 Documents (Results 1–32)

Nonlinear Fokker-Planck flows and their probabilistic counterparts. (English) Zbl 07863722

Interacting stochastic processes on sparse random graphs. (English) Zbl 1533.60181

Load balancing under strict compatibility constraints. (English) Zbl 1532.60197

Optimal control and stabilization for linear continuous-time mean-field systems with delay. (English) Zbl 07903449

A general stochastic maximum principle for mean-field controls with regime switching. (English) Zbl 1475.60140

A hierarchical mean field model of interacting spins. (English) Zbl 1471.58037

Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles. (English) Zbl 1448.35507

Recursive tree processes and the mean-field limit of stochastic flows. (English) Zbl 1446.82054

Analysis of large urn models with local mean-field interactions. (English) Zbl 1412.60113

About the entropic structure of detailed balanced multi-species cross-diffusion equations. (English) Zbl 1405.35082

Characterization of stochastic mean-field type \(\mathcal{H}\_\) index. (English) Zbl 1407.93356

On bounding exact models of epidemic spread on networks. (English) Zbl 1398.34067

A large scale analysis of unreliable stochastic networks. (English) Zbl 1391.60219

Path-space moderate deviation principles for the random field Curie-Weiss model. (English) Zbl 1390.60102

Choosing among heterogeneous server clouds. (English) Zbl 1368.60100

Metastability of non-reversible, mean-field Potts model with three spins. (English) Zbl 1360.82055

Modeling networks of spiking neurons as interacting processes with memory of variable length. (Modéliser les décharges de neurones par des processus en interactions avec une mémoire de longueur variable.) (English. French summary) Zbl 1357.92012

On a toy model of interacting neurons. (English. French summary) Zbl 1355.92014

Gradient flow structure for McKean-Vlasov equations on discrete spaces. (English) Zbl 1353.60084

Mean-field limits beyond ordinary differential equations. (English) Zbl 1346.68217

Hybrid behaviour of Markov population models. (English) Zbl 1336.68177

Finite horizon mean-field stochastic \(H_2/H_\infty\) control for continuous-time systems with \((x,v)\)-dependent noise. (English) Zbl 1395.93578

Task delegation in a peer-to-peer volunteer computing platform. (English) Zbl 1392.68098

Limits of relative entropies associated with weakly interacting particle systems. (English) Zbl 1321.60202

On spins and genes. (English) Zbl 1320.00038

Differential equation approximations of stochastic network processes: an operator semigroup approach. (English) Zbl 1483.47125

Pseudogap behavior in the infinite dimensional attractive Hubbard model. (English) Zbl 1259.82059

Mean field variational approximation for continuous-time Bayesian networks. (English) Zbl 1242.68215

Phase transitions in the queuing networks and the violation of the Poisson hypothesis. (English) Zbl 1155.82012

Mean field convergence of a model of multiple TCP connections through a buffer implementing RED. (English) Zbl 1094.60053

Poisson hypothesis for information networks. I. (English) Zbl 1111.82034

On the Hopfield neural networks and mean field theory. (English) Zbl 0869.68080

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