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Quantitative invertibility of non-Hermitian random matrices

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arxiv 2206.00601 v1 pith:KVTCBSZP submitted 2022-06-01 math.PR

Konstantin Tikhomirov This is my paper · ORCID
classification math.PR
keywords invertibilitymatricesnon-hermitianquantitativerandomanalysisapplicationscomputations
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The problem of estimating the smallest singular value of random square matrices is important in connection with matrix computations and analysis of the spectral distribution. In this survey, we consider recent developments in the study of quantitative invertibility in the non-Hermitian setting, and review some applications of this line of research.

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  1. Limiting spectral laws for sparse random circulant matrices

    math.PR 2025-04 conditional novelty 7.0 of 10

    For d-regular random G_n-circulant matrices, the ESD converges in expectation iff the order distribution of a uniform group element converges, and in probability iff that order law is a point mass.

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