Year: 2024
Type: preprint
Abstract: We consider the characteristic function of linear spectral statistics of generalized Wigner matrices. We provide an expansion of the characteristic function with error $\mathcal{O} ( N^{-1})$ around its limiting Gaussian form, and identify sub-leading non-Gaussian corrections of size $\mathcal{O} (N^{-1/2})$. Prior expansions with this error rate held only for Wigner matrices; only a weaker error rate was available for more general matrix ensembles. We provide some applications.
Source: arXiv (Cornell University)
Author: Landon, Benjamin
Institution: University of Toronto
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405876266