Sharp Concave Transport Rates for Spectral Measures of Powers of Random Matrices

报告人：黄璐静 教授

报告题目：Sharp Concave Transport Rates for Spectral Measures of Powers of Random Matrices

报告时间：2026年10月24日（周六）上午9：00

报告地点：云龙校区智华楼201报告厅

主办单位：数学与统计学院、数学研究院、科学技术研究院

报告人简介：

黄璐静，福建师范大学数学与统计学院教授，主要从事马氏过程与统计物理的研究。

报告摘要：

We study the concave transport cost between the empirical spectral measure of $m$th powers of Haar-distributed random matrices from the compact classical groups and the uniform measure on the unit circle. For $0<p<1$, let="" $\mathcal="" c_p$="" denote="" the="" transport="" cost="" with="" $d(x,y)^p$,="" $n_0$="" be="" number="" of="" nontrivial="" eigenvalues,="" and="" set="" $q="m\wedge" n$.="" we="" prove,="" uniformly="" in="" $m$,<="" p="">

\[

\mathbb E\mathcal C_p(\mu_{A,m},\lambda_{\mathbb T})

\asymp_p

\begin{cases}

N_0^{-p}, & 0<p<\frac12,\\< p="">

N_0^{-1/2}(1+\log q), & p=\frac12,\\

N_0^{-p}q^{p-\frac12}, & \frac12<p<1.< p="">

\end{cases}

\]

Thus $p=\frac12$ is the critical exponent for the dependence on the matrix power. The proof combines eigenvalue counting estimates with a multiscale comparison for the concave transport cost. This is based on a joint work with Bingyao Wu.