---
_id: '17154'
abstract:
- lang: eng
  text: 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 et al.
    (Random Matrices Theory Appl. 11(2):2250015, 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 given in the recent companion paper (Reker in Preprint, arXiv:2204.03419,
    2023). and thus allow identifying the fluctuation around the thermal value in
    certain thermalization problems.
article_number: '10'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Jana
  full_name: Reker, Jana
  id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
  last_name: Reker
citation:
  ama: Reker J. Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical
    Physics, Analysis and Geometry</i>. 2024;27(3). doi:<a href="https://doi.org/10.1007/s11040-024-09483-y">10.1007/s11040-024-09483-y</a>
  apa: Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices.
    <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href="https://doi.org/10.1007/s11040-024-09483-y">https://doi.org/10.1007/s11040-024-09483-y</a>
  chicago: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
    <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2024. <a
    href="https://doi.org/10.1007/s11040-024-09483-y">https://doi.org/10.1007/s11040-024-09483-y</a>.
  ieee: J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,”
    <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3. Springer Nature,
    2024.
  ista: Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices.
    Mathematical Physics, Analysis and Geometry. 27(3), 10.
  mla: Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.”
    <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3, 10, Springer
    Nature, 2024, doi:<a href="https://doi.org/10.1007/s11040-024-09483-y">10.1007/s11040-024-09483-y</a>.
  short: J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).
date_created: 2024-06-21T09:31:17Z
date_published: 2024-06-20T00:00:00Z
date_updated: 2025-09-08T07:58:43Z
day: '20'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1007/s11040-024-09483-y
ec_funded: 1
external_id:
  arxiv:
  - '2307.11029'
  isi:
  - '001251464300001'
file:
- access_level: open_access
  checksum: 7d04318d66f765621bdcb648378d458e
  content_type: application/pdf
  creator: cchlebak
  date_created: 2024-06-26T11:26:42Z
  date_updated: 2024-06-26T11:26:42Z
  file_id: '17175'
  file_name: 2024_MathPhysAnaGeo_Reker.pdf
  file_size: 1327596
  relation: main_file
  success: 1
file_date_updated: 2024-06-26T11:26:42Z
has_accepted_license: '1'
intvolume: '        27'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Mathematical Physics, Analysis and Geometry
publication_identifier:
  eissn:
  - 1572-9656
  issn:
  - 1385-0172
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
  record:
  - id: '17164'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Fluctuation moments for regular functions of Wigner Matrices
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 27
year: '2024'
...