An elementary mean-field approach to the spectral densities of random matrix ensembles

Wenping Cui, Jason W. Rocks and Pankaj Mehta

Physica A: Statistical Mechanics and its Applications, 2024, vol. 637, issue C

Abstract: We present a simple mean-field approach for calculating spectral densities for random matrix ensembles in the thermodynamic limit. Our approach is based on constructing a linear system of equations and calculating how the solutions to these equation change in response to a small perturbation using the zero-temperature cavity method. We illustrate the power of the method by providing simple analytic derivations of the Wigner Semi-circle Law for symmetric matrices, the Marchenko–Pastur Law for Wishart matrices, the spectral density for a product Wishart matrix composed of two square matrices, and the Circle and elliptic laws for real random matrices.

Keywords: Random matrices; Complex systems; cavity method; linear systems; Perturbation theory; Ecology (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:637:y:2024:i:c:s037843712400116x

DOI: 10.1016/j.physa.2024.129608

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