×

Random stochastic matrices from classical compact Lie groups and symmetric spaces. (English) Zbl 1459.15038

The authors compute some (spectral) quantities associated to some Lie-stochastic ensembles. Relevant numerical examples are also presented. The paper is well written.

MSC:

15B52 Random matrices (algebraic aspects)
15B51 Stochastic matrices
15B30 Matrix Lie algebras
22C05 Compact groups
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
60B20 Random matrices (probabilistic aspects)
62M15 Inference from stochastic processes and spectral analysis

References:

[1] Horvat, M., J. Stat. Mech., 2009, P07005 · Zbl 1456.82504
[2] Chafaï, D., J. Multivar. Anal., 101, 555 (2010) · Zbl 1187.15036
[3] Bordenave, C.; Caputo, P.; Chafaï, D., Probab. Theory Relat. Fields, 152, 751 (2012) · Zbl 1242.15034
[4] Innocentini, G. C. P.; Novaes, M., J. Stat. Mech., 2018, 103202 · Zbl 1456.60178
[5] Chatterjee, S.; Diaconis, P.; Sly, A.
[6] Cappellini, V.; Sommers, H.-J.; Bruzda, W.; Życzkowski, K., J. Phys. A: Math. Theor., 42, 365209 (2009) · Zbl 1179.15036
[7] Kottos, T.; Smilansky, U., Phys. Rev. Lett., 79, 4794 (1997)
[8] Tanner, G., J. Phys. A: Math. Gen., 33, 3567 (2000) · Zbl 0948.82016
[9] Tanner, G., J. Phys. A: Math. Gen., 34, 8485 (2001) · Zbl 0995.82031
[10] Berkolaiko, G., J. Phys. A: Math. Gen., 34, L319 (2001) · Zbl 1028.82007
[11] Życzkowski, K.; Kuś, M.; Słomczyński, W.; Sommers, H.-J., J. Phys. A: Math. Gen., 36, 3425 (2003) · Zbl 1038.15012
[12] Edelman, A., J. Multivar. Anal., 60, 203 (1997) · Zbl 0886.15024
[13] Kanzieper, E.; Akemann, G., Phys. Rev. Lett., 95, 230201 (2005)
[14] Edelman, A.; Kostlan, E.; Shub, M., J. Am. Math. Soc., 7, 247 (1994) · Zbl 0790.15017
[15] Pastur, L., Theor Math Phys, 10, 67-74 (1972)
[16] Erdös, L.; Ramirez, J.; Schlein, B.; Tao, T.; Vu, V.; Yau, H.-T., Math. Res. Lett., 17, 667 (2010) · Zbl 1277.15027
[17] Tao, T.; Vu, V., Acta Math, 206, 1, 127-204 (2011) · Zbl 1217.15043
[18] Collins, B., Int. Math. Res. Not., 2003, 17, 953 · Zbl 1049.60091
[19] Collins, B.; Śniady, P., Commun. Math. Phys., 264, 773 (2006) · Zbl 1108.60004
[20] Banica, T.; Collins, B.; Schlenker, J.-M., On polynomial integrals over the orthogonal group, J. Comb. Theory, Ser. A, 118, 778 (2011) · Zbl 1231.05282
[21] Matsumoto, S., Random Matrices: Theory Appl., 2, 1350001 (2013) · Zbl 1280.15020
[22] Mezzadri, F., Not. Am. Math. Soc., 54, 592 (2007) · Zbl 1156.22004
[23] Macdonald, I. G., Symmetric Functions and Hall Polynomials (1995) · Zbl 0899.05068
[24] Matsumoto, S.; Novak, J., Int. Math. Res. Not., 2013, 2, 362 · Zbl 1312.05143
[25] Berkolaiko, G.; Irving, J., J. Comb. Theory, Ser. A, 140, 1-37 (2016) · Zbl 1331.05005
[26] Matsumoto, S., Ramanujan J., 26, 69 (2011) · Zbl 1233.05214
[27] Berkolaiko, G.; Kuipers, J., J. Math. Phys., 54, 112103 (2013) · Zbl 1288.81048
[28] Novaes, M., J. Phys. A: Math. Theor., 50, 075201 (2017) · Zbl 1360.81176
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.