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Random stochastic matrices from classical compact Lie groups and symmetric spaces
- Source :
- Journal of Mathematical Physics 60, 123508 (2019)
- Publication Year :
- 2018
-
Abstract
- We consider random stochastic matrices $M$ with elements given by $M_{ij}=|U_{ij}|^2$, with $U$ being uniformly distributed on one of the classical compact Lie groups or associated symmetric spaces. We observe numerically that, for large dimensions, the spectral statistics of $M$, discarding the Perron-Frobenius eigenvalue $1$, are similar to those of the Gaussian Orthogonal ensemble for symmetric matrices and to those of the real Ginibre ensemble for non-symmetric matrices. Using Weingarten functions, we compute some spectral statistics that corroborate this universality. We also establish connections with some difficult enumerative problems involving permutations.<br />Comment: 27 pages, 4 figures
- Subjects :
- Mathematical Physics
Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Journal :
- Journal of Mathematical Physics 60, 123508 (2019)
- Publication Type :
- Report
- Accession number :
- edsarx.1807.10240
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1063/1.5099004