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Bernoulli Random Matrices

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arxiv 2112.05506 v1 pith:NNV7ZPTG submitted 2021-12-10 math.PR

Alice Guionnet (CNRS , UMPA-ENSL) This is my paper · ORCID
classification math.PR
keywords bernoullimatricesrandomadvancesbecomebreadthdescribingeigenvectors
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Random Matrix theory has become a field on its own with a breadth of new results, techniques, and ideas in the last thirty years. In these proceedings of the 8ECM 2021, I illustrate some of these advances by describing what is known about the spectrum and the eigenvectors of Bernoulli matrices.

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  1. Central limit theorems for linear spectral statistics of inhomogeneous random graphs with graphon limits

    math.PR 2024-12 conditional novelty 8.0 of 10

    For inhomogeneous random graphs with a graphon variance profile, the traces of powers of the adjacency matrix, suitably rescaled, converge to Gaussian processes with covariances expressible as graphon homomorphism densities.

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