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Random matrix theory over finite fields: a survey

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arxiv math/0003195 v2 pith:QVFOXDO2 submitted 2000-03-28 math.GR math.COmath.PR

Jason Fulman This is my paper · ORCID
classification math.GRmath.COmath.PR
keywords theoryfinitefunctionrandomsurveybeautifulchainsclasses
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First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful. Connections are made with symmetric function theory, Markov chains, potential theory, Rogers-Ramanujan type identities, quivers, and various measures on partitions.

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  1. Groupoid Cardinality and Random Permutations

    math.CT 2024-12 accept novelty 6.0 of 10

    The Cycle Length Lemma for random permutations is derived from an equivalence of groupoids, giving a categorified proof of a known result.

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