arXiv:2307.11029 Abstract | arXiv Analytics

arXiv:2307.11029 [math.PR]Abstract References Reviews Resources

Fluctuation Moments for Regular Functions of Wigner Matrices

Published 2023-07-20Version 1

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].

Comments: 52 pages (including appendix), 20 figures

Categories: math.PR, math.CO, math.OA

Subjects: 60B20, 15B52, 46L54

Keywords: wigner matrices, fluctuation moments, regular functions, functional central limit theorem, second-order free probability theory

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