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Local and global universality of random matrix cokernels

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arxiv 2210.08526 v1 pith:E4Z4BONY submitted 2022-10-16 math.PR math.COmath.NT

Hoi H. Nguyen , Melanie Matchett Wood This is my paper · ORCID
classification math.PRmath.COmath.NT
keywords randomuniversalitycokernelsgloballocalmatrixmodelsanswering
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In this paper we study the cokernels of various random integral matrix models, including random symmetric, random skew-symmetric, and random Laplacian matrices. We provide a systematic method to establish universality under very general randomness assumption. Our highlights include both local and global universality of the cokernel statistics of all these models. In particular, we find the probability that a sandpile group of an Erdos-Renyi random graph is cyclic, answering a question of Lorenzini from 2008.

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  1. Non-Archimedean GUE corners and Hecke modules

    math.PR 2024-12 accept novelty 8.0 of 10

    The joint distribution of singular numbers of all principal corners of a Haar-random p-adic Hermitian or alternating matrix is a (formal) Hall-Littlewood process.

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