Heat Kernel Empirical Laws on UN and GLN
نویسنده
چکیده
This paper studies the empirical laws of eigenvalues and singular values for random matrices drawn from the heat kernel measures on the unitary groups UN and the general linear groups GLN , for N ∈ N. It establishes the strongest known convergence results for the empirical eigenvalues in the UN case, and the first known almost sure convergence results for the eigenvalues and singular values in the GLN case. The limit noncommutative distribution associated to the heat kernel measure on GLN is identified as the projection of a flow on an infinite dimensional polynomial space. These results are then strengthened from variance estimates to L estimates for even integers p.
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