---
_id: '1207'
abstract:
- lang: eng
  text: The eigenvalue distribution of the sum of two large Hermitian matrices, when
    one of them is conjugated by a Haar distributed unitary matrix, is asymptotically
    given by the free convolution of their spectral distributions. We prove that this
    convergence also holds locally in the bulk of the spectrum, down to the optimal
    scales larger than the eigenvalue spacing. The corresponding eigenvectors are
    fully delocalized. Similar results hold for the sum of two real symmetric matrices,
    when one is conjugated by Haar orthogonal matrix.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- 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: Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal
    scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a
    href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random
    matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
    of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>.
    Springer, 2017. <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
    on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no.
    3. Springer, pp. 947–990, 2017.
  ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices
    on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.
  mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.”
    <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017,
    pp. 947–90, doi:<a href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349
    (2017) 947–990.
date_created: 2018-12-11T11:50:43Z
date_published: 2017-02-01T00:00:00Z
date_updated: 2025-07-10T11:50:22Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2805-6
ec_funded: 1
external_id:
  isi:
  - '000393696700005'
file:
- access_level: open_access
  checksum: ddff79154c3daf27237de5383b1264a9
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  creator: system
  date_created: 2018-12-12T10:14:47Z
  date_updated: 2020-07-14T12:44:39Z
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file_date_updated: 2020-07-14T12:44:39Z
fulldoi: https://doi.org/10.1007/s00220-016-2805-6
has_accepted_license: '1'
intvolume: '       349'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 947 - 990
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - 0010-3616
publication_status: published
publisher: Springer
publist_id: '6141'
pubrep_id: '722'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law of addition of random matrices on optimal scale
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 349
year: '2017'
...