关于随机矩阵的热流猜想
On the heat flow conjecture for random matrices
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中文总结 AI 辅助
该研究证明了Hall-Ho的随机矩阵热流猜想的一般情况，发现复Ginibre矩阵热流演化后特征多项式零点的经验测度几乎必然收敛到半圆律。
中文摘要 AI 辅助
我们证明了Hall-Ho提出的随机矩阵热流猜想的一般情况，具体而言，复Ginibre矩阵经热流演化后的特征多项式零点的经验测度几乎必然收敛到半圆律。
英文摘要
We prove two families of distinguished cases of the heat flow conjecture for random matrices of Hall-Ho: elliptic Gaussian sources with planar targets, and deterministic Hermitian sources with targets on the boundary of the covariance disk. In particular, the empirical zero measure of the heat-evolved characteristic polynomial of a complex Ginibre matrix converges almost surely to the semicircle law. The strategy of the proof is to transfer estimates for the corresponding well-understood Gaussian matrix ensembles, through exact heat identities, into control of the zeros of the heat-evolved characteristic polynomials.
