---
_id: '2782'
abstract:
- lang: eng
  text: We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2},
    where X and Y have independent entries with zero mean and variance one. These
    matrices are the natural generalization of the Gaussian case, which are known
    as MANOVA matrices and which have joint eigenvalue density given by the third
    classical ensemble, the Jacobi ensemble. We show that, away from the spectral
    edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble
    even on the shortest possible scales of order 1/n (up to log n factors). This
    result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur
    law for general MANOVA matrices.
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: Brendan
  full_name: Farrell, Brendan
  last_name: Farrell
citation:
  ama: Erdös L, Farrell B. Local eigenvalue density for general MANOVA matrices. <i>Journal
    of Statistical Physics</i>. 2013;152(6):1003-1032. doi:<a href="https://doi.org/10.1007/s10955-013-0807-8">10.1007/s10955-013-0807-8</a>
  apa: Erdös, L., &#38; Farrell, B. (2013). Local eigenvalue density for general MANOVA
    matrices. <i>Journal of Statistical Physics</i>. Springer. <a href="https://doi.org/10.1007/s10955-013-0807-8">https://doi.org/10.1007/s10955-013-0807-8</a>
  chicago: Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General
    MANOVA Matrices.” <i>Journal of Statistical Physics</i>. Springer, 2013. <a href="https://doi.org/10.1007/s10955-013-0807-8">https://doi.org/10.1007/s10955-013-0807-8</a>.
  ieee: L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,”
    <i>Journal of Statistical Physics</i>, vol. 152, no. 6. Springer, pp. 1003–1032,
    2013.
  ista: Erdös L, Farrell B. 2013. Local eigenvalue density for general MANOVA matrices.
    Journal of Statistical Physics. 152(6), 1003–1032.
  mla: Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA
    Matrices.” <i>Journal of Statistical Physics</i>, vol. 152, no. 6, Springer, 2013,
    pp. 1003–32, doi:<a href="https://doi.org/10.1007/s10955-013-0807-8">10.1007/s10955-013-0807-8</a>.
  short: L. Erdös, B. Farrell, Journal of Statistical Physics 152 (2013) 1003–1032.
corr_author: '1'
date_created: 2018-12-11T11:59:34Z
date_published: 2013-07-18T00:00:00Z
date_updated: 2025-09-29T14:07:43Z
day: '18'
department:
- _id: LaEr
doi: 10.1007/s10955-013-0807-8
external_id:
  arxiv:
  - '1207.0031'
  isi:
  - '000323203800001'
intvolume: '       152'
isi: 1
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1207.0031
month: '07'
oa: 1
oa_version: Preprint
page: 1003 - 1032
publication: Journal of Statistical Physics
publication_status: published
publisher: Springer
publist_id: '4107'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local eigenvalue density for general MANOVA matrices
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 152
year: '2013'
...
---
_id: '2837'
abstract:
- lang: eng
  text: We consider a general class of N × N random matrices whose entries hij are
    independent up to a symmetry constraint, but not necessarily identically distributed.
    Our main result is a local semicircle law which improves previous results [17]
    both in the bulk and at the edge. The error bounds are given in terms of the basic
    small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality
    of the local n-point correlation functions in the bulk spectrum for a class of
    matrices whose entries do not have comparable variances, including random band
    matrices with band width W ≫N1-εn with some εn &gt; 0 and with a negligible mean-field
    component. In addition, we provide a coherent and pedagogical proof of the local
    semicircle law, streamlining and strengthening previous arguments from [17, 19,
    6].
article_processing_charge: No
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Antti
  full_name: Knowles, Antti
  last_name: Knowles
- first_name: Horng
  full_name: Yau, Horng
  last_name: Yau
- first_name: Jun
  full_name: Yin, Jun
  last_name: Yin
citation:
  ama: Erdös L, Knowles A, Yau H, Yin J. The local semicircle law for a general class
    of random matrices. <i>Electronic Journal of Probability</i>. 2013;18(59):1-58.
    doi:<a href="https://doi.org/10.1214/EJP.v18-2473">10.1214/EJP.v18-2473</a>
  apa: Erdös, L., Knowles, A., Yau, H., &#38; Yin, J. (2013). The local semicircle
    law for a general class of random matrices. <i>Electronic Journal of Probability</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/EJP.v18-2473">https://doi.org/10.1214/EJP.v18-2473</a>
  chicago: Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “The Local Semicircle
    Law for a General Class of Random Matrices.” <i>Electronic Journal of Probability</i>.
    Institute of Mathematical Statistics, 2013. <a href="https://doi.org/10.1214/EJP.v18-2473">https://doi.org/10.1214/EJP.v18-2473</a>.
  ieee: L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a
    general class of random matrices,” <i>Electronic Journal of Probability</i>, vol.
    18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.
  ista: Erdös L, Knowles A, Yau H, Yin J. 2013. The local semicircle law for a general
    class of random matrices. Electronic Journal of Probability. 18(59), 1–58.
  mla: Erdös, László, et al. “The Local Semicircle Law for a General Class of Random
    Matrices.” <i>Electronic Journal of Probability</i>, vol. 18, no. 59, Institute
    of Mathematical Statistics, 2013, pp. 1–58, doi:<a href="https://doi.org/10.1214/EJP.v18-2473">10.1214/EJP.v18-2473</a>.
  short: L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 18
    (2013) 1–58.
date_created: 2018-12-11T11:59:51Z
date_published: 2013-05-29T00:00:00Z
date_updated: 2025-09-29T13:46:52Z
day: '29'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1214/EJP.v18-2473
external_id:
  isi:
  - '000319561600001'
file:
- access_level: open_access
  checksum: aac9e52a00cb2f5149dc9e362b5ccf44
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:15:46Z
  date_updated: 2020-07-14T12:45:50Z
  file_id: '5169'
  file_name: IST-2016-406-v1+1_2473-13759-1-PB.pdf
  file_size: 651497
  relation: main_file
file_date_updated: 2020-07-14T12:45:50Z
has_accepted_license: '1'
intvolume: '        18'
isi: 1
issue: '59'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1-58
publication: Electronic Journal of Probability
publication_status: published
publisher: Institute of Mathematical Statistics
publist_id: '3962'
pubrep_id: '406'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The local semicircle law for a general class of random 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 18
year: '2013'
...