Fluctuation Moments for Regular Functions of Wigner Matrices

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, Peché, 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].

arXiv comment52 pages (including appendix), 20 figures

References in corpus (5)

• On Asymptotic Properties of Large Random Matrices with Independent Entries
• Asymptotic expansion of beta matrix models in the one-cut regime
• Fluctuations of linear eigenvalue statistics of $\beta$ matrix models in the multi-cut regime
• Regularity conditions in the CLT for linear eigenvalue statistics of Wigner matrices
• Real second-order freeness and the asymptotic real second-order freeness of several real matrix ensembles

Cited by in corpus (1)

• Multi-Point Functional Central Limit Theorem for Wigner Matrices