Year: 2026
Type: preprint
Abstract: We consider linear statistics $\sum_{k=1}^N f(x_k)$ of a Gaussian $\b$-ensemble. Following the work of \cite{LaSo22}, which was concerned only with Wigner matrices, we extend their results for general $\b$. In particular, we show that the CLT holds for any $f \in H^{1/2 + \e}$. The novel input which was not used in \cite{LaSo22} is the Helffer-Sjöstrand representation for the covariance, first appearing the random matrix context in \cite{ErYa15}, coupled with characteristic flow estimates for DBM, first appearing in \cite{Bo22}.
Source: arXiv (Cornell University)
Author: Zhang, Albert
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223022197