---
_id: '1508'
abstract:
- lang: eng
  text: We consider generalized Wigner ensembles and general β-ensembles with analytic
    potentials for any β ≥ 1. The recent universality results in particular assert
    that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum
    are universal in the sense that they coincide with those of the corresponding
    Gaussian β-ensembles. In this article, we show that local averaging is not necessary
    for this result, i.e. we prove that the single gap distributions in the bulk are
    universal. In fact, with an additional step, our result can be extended to any
    C4(ℝ) potential.
article_processing_charge: No
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
citation:
  ama: Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. <i>Journal
    of the European Mathematical Society</i>. 2015;17(8):1927-2036. doi:<a href="https://doi.org/10.4171/JEMS/548">10.4171/JEMS/548</a>
  apa: Erdös, L., &#38; Yau, H. (2015). Gap universality of generalized Wigner and
    β ensembles. <i>Journal of the European Mathematical Society</i>. EMS Press. <a
    href="https://doi.org/10.4171/JEMS/548">https://doi.org/10.4171/JEMS/548</a>
  chicago: Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and
    β Ensembles.” <i>Journal of the European Mathematical Society</i>. EMS Press,
    2015. <a href="https://doi.org/10.4171/JEMS/548">https://doi.org/10.4171/JEMS/548</a>.
  ieee: L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,”
    <i>Journal of the European Mathematical Society</i>, vol. 17, no. 8. EMS Press,
    pp. 1927–2036, 2015.
  ista: Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles.
    Journal of the European Mathematical Society. 17(8), 1927–2036.
  mla: Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β
    Ensembles.” <i>Journal of the European Mathematical Society</i>, vol. 17, no.
    8, EMS Press, 2015, pp. 1927–2036, doi:<a href="https://doi.org/10.4171/JEMS/548">10.4171/JEMS/548</a>.
  short: L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015)
    1927–2036.
das_tickbox: '1'
date_created: 2018-12-11T11:52:26Z
date_published: 2015-08-01T00:00:00Z
date_updated: 2026-07-06T11:55:30Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/JEMS/548
external_id:
  arxiv:
  - '1211.3786'
  isi:
  - '000360822900003'
fulldoi: https://doi.org/10.4171/JEMS/548
intvolume: '        17'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1211.3786
month: '08'
oa: 1
oa_version: Preprint
page: 1927 - 2036
publication: Journal of the European Mathematical Society
publication_status: published
publisher: EMS Press
publist_id: '5669'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Gap universality of generalized Wigner and β ensembles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 17
year: '2015'
...