Speaker: 张纪元，华南理工大学

Title: Markov-Krein correspondence in orbital $\beta$-projection

Language: Chinese

Time & Venue: 2026.10.23 16:00-17:00 南楼N613

Abstract: The Markov--Krein correspondence relates a probability measure to a Rayleigh distribution through an exponential transform of its Cauchy transform.

Fujie and Hasebe proved that the empirical spectral measure of a unitarily invariant Hermitian matrix and the Rayleigh distribution of its principal minor satisfy this correspondence asymptotically under convergence of moments. In this paper, we extend this result to orbital $\beta$-projections for arbitrary $\beta>0$, where we replace the moment assumption by weak convergence of the empirical measures and introduce a weak$^*$ topology on $W^{1,1}(\R)^*$ that naturally captures the convergence of Rayleigh distributions. In particular, our result covers the orthogonal and symplectic analogues of the Fujie--Hasebe theorem corresponding to $\beta=1$ and $\beta=4$.