---
_id: '615'
abstract:
- lang: eng
  text: We show that the Dyson Brownian Motion exhibits local universality after a
    very short time assuming that local rigidity and level repulsion of the eigenvalues
    hold. These conditions are verified, hence bulk spectral universality is proven,
    for a large class of Wigner-like matrices, including deformed Wigner ensembles
    and ensembles with non-stochastic variance matrices whose limiting densities differ
    from Wigner's semicircle law.
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Erdös L, Schnelli K. Universality for random matrix flows with time dependent
    density. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>.
    2017;53(4):1606-1656. doi:<a href="https://doi.org/10.1214/16-AIHP765">10.1214/16-AIHP765</a>
  apa: Erdös, L., &#38; Schnelli, K. (2017). Universality for random matrix flows
    with time dependent density. <i>Annales de l’institut Henri Poincare (B) Probability
    and Statistics</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/16-AIHP765">https://doi.org/10.1214/16-AIHP765</a>
  chicago: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows
    with Time Dependent Density.” <i>Annales de l’institut Henri Poincare (B) Probability
    and Statistics</i>. Institute of Mathematical Statistics, 2017. <a href="https://doi.org/10.1214/16-AIHP765">https://doi.org/10.1214/16-AIHP765</a>.
  ieee: L. Erdös and K. Schnelli, “Universality for random matrix flows with time
    dependent density,” <i>Annales de l’institut Henri Poincare (B) Probability and
    Statistics</i>, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656,
    2017.
  ista: Erdös L, Schnelli K. 2017. Universality for random matrix flows with time
    dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics.
    53(4), 1606–1656.
  mla: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with
    Time Dependent Density.” <i>Annales de l’institut Henri Poincare (B) Probability
    and Statistics</i>, vol. 53, no. 4, Institute of Mathematical Statistics, 2017,
    pp. 1606–56, doi:<a href="https://doi.org/10.1214/16-AIHP765">10.1214/16-AIHP765</a>.
  short: L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability
    and Statistics 53 (2017) 1606–1656.
date_created: 2018-12-11T11:47:30Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2021-01-12T08:06:22Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/16-AIHP765
ec_funded: 1
intvolume: '        53'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1504.00650
month: '11'
oa: 1
oa_version: Submitted Version
page: 1606 - 1656
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
  issn:
  - '02460203'
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '7189'
quality_controlled: '1'
scopus_import: 1
status: public
title: Universality for random matrix flows with time dependent density
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 53
year: '2017'
...