an:07177380
Zbl 07177380
Oliveira, Lucas H.; Novaes, Marcel
Random stochastic matrices from classical compact Lie groups and symmetric spaces
EN
J. Math. Phys. 60, No. 12, 123508, 17 p. (2019).
00447469
2019
j
15B52 15B51 15B30 22C05 32M15 60B20 62M15
random stochastic matrices; symmetric spaces; Perron-Frobenius eigenvalue; Ginibre ensemble
Summary: 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 some of the 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 nonsymmetric matrices. We compute some spectral statistics using Weingarten functions and establish connections with some difficult enumerative problems involving permutations.\par{\copyright 2019 American Institute of Physics}