Real symmetric random matrices and replicas

TL;DR

This paper applies the replica formalism to analyze various ensembles of large symmetric random matrices, generalizing results for Laplacian matrices with Wigner-rescaling to arbitrary distributions.

Contribution

It extends the replica analysis to a broad class of symmetric random matrices, including those with arbitrary entry distributions.

Findings

Generalized Laplacian matrix results to arbitrary distributions

Applied replica formalism to large-N symmetric matrices

Provided insights into spectral properties of random matrices

Abstract

Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.