Fluctuation Moments for Regular Functions of Wigner Matrices
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917778770886656 |
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| author | Reker, Jana |
| author_facet | Reker, Jana |
| contents | 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]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_11029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fluctuation Moments for Regular Functions of Wigner Matrices Reker, Jana Probability Combinatorics Operator Algebras 60B20, 15B52, 46L54 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]. |
| title | Fluctuation Moments for Regular Functions of Wigner Matrices |
| topic | Probability Combinatorics Operator Algebras 60B20, 15B52, 46L54 |
| url | https://arxiv.org/abs/2307.11029 |