Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for product of two Gaussian matrices

Abstract

We provide a proof to a recent conjecture by Forrester [2014 J. Phys. A: Math. Theor. 47, 065202] regarding the algebraic and arithmetic structure of Meijer G-functions which appear in the expression for probability of all eigenvalues real for product of two real Gaussian matrices. In the process we come across several interesting identities involving Meijer G-functions.

Published version; 8 pages, 1 figure

References in corpus (4)

• Recent exact and asymptotic results for products of independent random matrices
• Singular value statistics of matrix products with truncated unitary matrices
• The Lyapunov exponent of products of random $2\times 2$ matrices close to the identity
• Random matrix ensembles involving Gaussian Wigner and Wishart matrices, and biorthogonal structure

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• Real eigenvalue statistics for products of asymmetric real Gaussian matrices
• How many eigenvalues of a product of truncated orthogonal matrices are real?