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Large deviations for macroscopic observables of heavy-tailed matrices
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We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy 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.
Forward citations
Cited by 2 Pith papers
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Random permutation-plus-diagonal matrices reproduce the natural-generator spectral measure of lamplighter groups, with a CLT for Γ=Z.
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