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The Hall-Ho Heat Flow Conjecture for Random Matrices

Probability & statistics · posed by Brian Hall, Ching-Wei Ho · partial

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Statement

Hall and Ho conjectured how the zeros of the heat-flow-evolved characteristic polynomial of a random matrix behave in the large-nn limit. General cases are proved; in particular, for a complex Ginibre matrix the empirical measure of those zeros converges almost surely to the semicircle law.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Theodoros Assiotis, using ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

    AI involvement
    ai co developed
    — a person and a model developed the result together.

    An unusually direct disclosure: "In the course of the research presented here I have been using AI tools extensively, most significantly ChatGPT Pro 5.5 and ChatGPT 5.6 Sol Ultra for ideation, technical help, editing and checking the proofs and general editing and proofreading of the manuscript, at the level of a co-author. All mistakes are my own responsibility." The phrase "at the level of a co-author" is the author's own.

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