The Hall-Ho Heat Flow Conjecture for Random Matrices
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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- 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.
Context
Proves general cases of the conjecture rather than every case.
A named conjecture in the active Hall-Ho line on heat flow and random matrix zeros, specialist but with a clear attribution and a real following.
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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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