The Hall-Ho Heat Flow Conjecture for Random Matrices
Prior state unknown→proved
Proves general cases of the conjecture rather than every case.
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probability-statistics / Random matrix theory
The Hall-Ho Heat Flow Conjecture for Random Matrices
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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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.
Proves general cases of the conjecture rather than every case.
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