Large deviations for macroscopic observables of heavy-tailed matrices

2024/09/21 by Bordenave, Charles, Guionnet, Alice, Male, Camille · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.14027

Abstract

We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the Lévy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries per row. By representing these matrices as weighted graphs, we derive a large deviations principle for key macroscopic observables. Specifically, we focus on the empirical distribution of eigenvalues, the joint neighborhood distribution, and the joint traffic distribution. As an application, we define a notion of microstates entropy for traffic distributions which is additive for free traffic convolution.

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• LDP for the largest eigenvalue of Kronecker random matrices
• Sparse graphs and their Benjamini-Schramm limits: a spectral tour

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