---
_id: '10732'
abstract:
- lang: eng
  text: We compute the deterministic approximation of products of Sobolev functions
    of large Wigner matrices W and provide an optimal error bound on their fluctuation
    with very high probability. This generalizes Voiculescu's seminal theorem from
    polynomials to general Sobolev functions, as well as from tracial quantities to
    individual matrix elements. Applying the result to eitW for large t, we obtain
    a precise decay rate for the overlaps of several deterministic matrices with temporally
    well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
    effect of the unitary group generated by Wigner matrices.
acknowledgement: We compute the deterministic approximation of products of Sobolev
  functions of large Wigner matrices W and provide an optimal error bound on their
  fluctuation with very high probability. This generalizes Voiculescu's seminal theorem
  from polynomials to general Sobolev functions, as well as from tracial quantities
  to individual matrix elements. Applying the result to  for large t, we obtain a
  precise decay rate for the overlaps of several deterministic matrices with temporally
  well separated Heisenberg time evolutions; thus we demonstrate the thermalisation
  effect of the unitary group generated by Wigner matrices.
article_number: '109394'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Dominik J
  full_name: Schröder, Dominik J
  id: 408ED176-F248-11E8-B48F-1D18A9856A87
  last_name: Schröder
  orcid: 0000-0002-2904-1856
citation:
  ama: Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal
    of Functional Analysis</i>. 2022;282(8). doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for
    Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation
    for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a
    href="https://doi.org/10.1016/j.jfa.2022.109394">https://doi.org/10.1016/j.jfa.2022.109394</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,”
    <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices.
    Journal of Functional Analysis. 282(8), 109394.
  mla: Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal
    of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.jfa.2022.109394">10.1016/j.jfa.2022.109394</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282
    (2022).
corr_author: '1'
date_created: 2022-02-06T23:01:30Z
date_published: 2022-04-15T00:00:00Z
date_updated: 2024-10-09T21:01:33Z
day: '15'
ddc:
- '500'
department:
- _id: LaEr
doi: 10.1016/j.jfa.2022.109394
external_id:
  arxiv:
  - '2102.09975'
  isi:
  - '000781239100004'
file:
- access_level: open_access
  checksum: b75fdad606ab507dc61109e0907d86c0
  content_type: application/pdf
  creator: dernst
  date_created: 2022-07-29T07:22:08Z
  date_updated: 2022-07-29T07:22:08Z
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file_date_updated: 2022-07-29T07:22:08Z
has_accepted_license: '1'
intvolume: '       282'
isi: 1
issue: '8'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
  eissn:
  - 1096-0783
  issn:
  - 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Thermalisation for 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 282
year: '2022'
...