Real symmetric random matrices and paths counting

Abstract

Exact evaluation of $<\mathrm{Tr}{S}^p>$ is here performed for real symmetric matrices $S$ of arbitrary order $n$, up to some integer $p$, where the matrix entries are independent identically distributed random variables, with an arbitrary probability distribution. These expectations are polynomials in the moments of the matrix entries ; they provide useful information on the spectral density of the ensemble in the large $n$ limit. They also are a straightforward tool to examine a variety of rescalings of the entries in the large $n$ limit.

arXiv comment23 pages, 10 figures, revised paper

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Cited by in corpus (3)

• A unifying model for random matrix theory in arbitrary space dimensions
• Real symmetric random matrices and replicas
• Comment on "Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices" by G.S. Dhesi and M. Ausloos