Fluctuation Moments for Regular Functions of Wigner Matrices
Probability
2024-09-19 v1 Combinatorics
Operator Algebras
Abstract
We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of [Male, Mingo, Pech\'e, Speicher 2022], showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem obtained recently in the companion paper [Reker 2023].
Keywords
Cite
@article{arxiv.2307.11029,
title = {Fluctuation Moments for Regular Functions of Wigner Matrices},
author = {Jana Reker},
journal= {arXiv preprint arXiv:2307.11029},
year = {2024}
}
Comments
52 pages (including appendix), 20 figures