The Hall-Ho Heat Flow Conjecture for Random Matrices
partialconfidence 70%
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Precise statement
Hall and Ho conjectured how the zeros of the heat-flow-evolved characteristic polynomial of a random matrix behave in the large-$n$ 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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What AI did
ChatGPT Pro 5.5, ChatGPT 5.6 Sol Ultra
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.