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Real symmetric random matrices and paths counting

Giovanni M. Cicuta
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Abstract

Exact evaluation of $<{\rm Tr} S^p>$ 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.

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Giovanni M. Cicuta. 2005-04-21. Real symmetric random matrices and paths counting. https://doi.org/10.1103/physreve.72.026122

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