---
_id: '6182'
abstract:
- lang: eng
  text: "We consider large random matrices with a general slowly decaying correlation
    among its entries. We prove universality of the local eigenvalue statistics and
    optimal local laws for the resolvent away from the spectral edges, generalizing
    the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and
    random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019),
    293–373] to allow slow correlation decay and arbitrary expectation. The main novel
    tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."
article_number: e8
article_processing_charge: No
article_type: original
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: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
- 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: Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay.
    <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a>
  apa: Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with
    slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a>
  chicago: Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices
    with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University
    Press, 2019. <a href="https://doi.org/10.1017/fms.2019.2">https://doi.org/10.1017/fms.2019.2</a>.
  ieee: L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation
    decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press,
    2019.
  ista: Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation
    decay. Forum of Mathematics, Sigma. 7, e8.
  mla: Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum
    of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a
    href="https://doi.org/10.1017/fms.2019.2">10.1017/fms.2019.2</a>.
  short: L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).
corr_author: '1'
date_created: 2019-03-28T09:05:23Z
date_published: 2019-03-26T00:00:00Z
date_updated: 2026-07-29T13:46:19Z
day: '26'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1017/fms.2019.2
ec_funded: 1
external_id:
  arxiv:
  - '1705.10661'
  isi:
  - '000488847100001'
file:
- access_level: open_access
  checksum: 933a472568221c73b2c3ce8c87bf6d15
  content_type: application/pdf
  creator: dernst
  date_created: 2019-09-17T14:24:13Z
  date_updated: 2020-07-14T12:47:22Z
  file_id: '6883'
  file_name: 2019_Forum_Erdoes.pdf
  file_size: 1520344
  relation: main_file
file_date_updated: 2020-07-14T12:47:22Z
fulldoi: https://doi.org/10.1017/fms.2019.2
has_accepted_license: '1'
intvolume: '         7'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
related_material:
  record:
  - id: '6179'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Random matrices with slow correlation decay
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 7
year: '2019'
...