---
_id: '11135'
abstract:
- lang: eng
  text: We consider a correlated NxN Hermitian random matrix with a polynomially decaying
    metric correlation structure. By calculating the trace of the moments of the matrix
    and using the summable decay of the cumulants, we show that its operator norm
    is stochastically dominated by one.
article_number: '2250036'
article_processing_charge: No
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. On the operator norm of a Hermitian random matrix with correlated
    entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href="https://doi.org/10.1142/s2010326322500368">10.1142/s2010326322500368</a>'
  apa: 'Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated
    entries. <i>Random Matrices: Theory and Applications</i>. World Scientific. <a
    href="https://doi.org/10.1142/s2010326322500368">https://doi.org/10.1142/s2010326322500368</a>'
  chicago: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
    Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific, 2022.
    <a href="https://doi.org/10.1142/s2010326322500368">https://doi.org/10.1142/s2010326322500368</a>.'
  ieee: 'J. Reker, “On the operator norm of a Hermitian random matrix with correlated
    entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World
    Scientific, 2022.'
  ista: 'Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated
    entries. Random Matrices: Theory and Applications. 11(4), 2250036.'
  mla: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
    Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036,
    World Scientific, 2022, doi:<a href="https://doi.org/10.1142/s2010326322500368">10.1142/s2010326322500368</a>.'
  short: 'J. Reker, Random Matrices: Theory and Applications 11 (2022).'
date_created: 2022-04-08T07:11:12Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-08-03T06:32:22Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326322500368
external_id:
  arxiv:
  - '2103.03906'
  isi:
  - '000848873800001'
intvolume: '        11'
isi: 1
issue: '4'
keyword:
- Discrete Mathematics and Combinatorics
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2103.03906'
month: '10'
oa: 1
oa_version: Preprint
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the operator norm of a Hermitian random matrix with correlated entries
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 11
year: '2022'
...
---
_id: '5971'
abstract:
- lang: eng
  text: "We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices
    H=H∗ with centered independent entries and with a general matrix of variances
    Sxy=\U0001D53C∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of
    the support of the self-consistent density of states. We establish a bound on
    this maximum in terms of norms of powers of S that substantially improves the
    earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality
    for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727].
    The key element of the proof is an effective Markov chain approximation for the
    contributions of the weighted Dyck paths appearing in the iterative solution of
    the corresponding Dyson equation."
article_number: '1950009'
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: Peter
  full_name: Mühlbacher, Peter
  last_name: Mühlbacher
citation:
  ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices.
    <i>Random matrices: Theory and applications</i>. 2018. doi:<a href="https://doi.org/10.1142/s2010326319500096">10.1142/s2010326319500096</a>'
  apa: 'Erdös, L., &#38; Mühlbacher, P. (2018). Bounds on the norm of Wigner-type
    random matrices. <i>Random Matrices: Theory and Applications</i>. World Scientific
    Publishing. <a href="https://doi.org/10.1142/s2010326319500096">https://doi.org/10.1142/s2010326319500096</a>'
  chicago: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type
    Random Matrices.” <i>Random Matrices: Theory and Applications</i>. World Scientific
    Publishing, 2018. <a href="https://doi.org/10.1142/s2010326319500096">https://doi.org/10.1142/s2010326319500096</a>.'
  ieee: 'L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,”
    <i>Random matrices: Theory and applications</i>. World Scientific Publishing,
    2018.'
  ista: 'Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices.
    Random matrices: Theory and applications., 1950009.'
  mla: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random
    Matrices.” <i>Random Matrices: Theory and Applications</i>, 1950009, World Scientific
    Publishing, 2018, doi:<a href="https://doi.org/10.1142/s2010326319500096">10.1142/s2010326319500096</a>.'
  short: 'L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).'
date_created: 2019-02-13T10:40:54Z
date_published: 2018-09-26T00:00:00Z
date_updated: 2023-09-19T14:24:05Z
day: '26'
department:
- _id: LaEr
doi: 10.1142/s2010326319500096
ec_funded: 1
external_id:
  arxiv:
  - '1802.05175'
  isi:
  - '000477677200002'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1802.05175
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: 'Random matrices: Theory and applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bounds on the norm of Wigner-type random matrices
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...