---
_id: '12707'
abstract:
- lang: eng
  text: We establish precise right-tail small deviation estimates for the largest
    eigenvalue of real symmetric and complex Hermitian matrices whose entries are
    independent random variables with uniformly bounded moments. The proof relies
    on a Green function comparison along a continuous interpolating matrix flow for
    a long time. Less precise estimates are also obtained in the left tail.
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: Yuanyuan
  full_name: Xu, Yuanyuan
  id: 7902bdb1-a2a4-11eb-a164-c9216f71aea3
  last_name: Xu
  orcid: 0000-0003-1559-1205
citation:
  ama: Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner
    matrices. <i>Bernoulli</i>. 2023;29(2):1063-1079. doi:<a href="https://doi.org/10.3150/22-BEJ1490">10.3150/22-BEJ1490</a>
  apa: Erdös, L., &#38; Xu, Y. (2023). Small deviation estimates for the largest eigenvalue
    of Wigner matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics
    and Probability. <a href="https://doi.org/10.3150/22-BEJ1490">https://doi.org/10.3150/22-BEJ1490</a>
  chicago: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
    Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical
    Statistics and Probability, 2023. <a href="https://doi.org/10.3150/22-BEJ1490">https://doi.org/10.3150/22-BEJ1490</a>.
  ieee: L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue
    of Wigner matrices,” <i>Bernoulli</i>, vol. 29, no. 2. Bernoulli Society for Mathematical
    Statistics and Probability, pp. 1063–1079, 2023.
  ista: Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue
    of Wigner matrices. Bernoulli. 29(2), 1063–1079.
  mla: Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest
    Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society
    for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href="https://doi.org/10.3150/22-BEJ1490">10.3150/22-BEJ1490</a>.
  short: L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.
date_created: 2023-03-05T23:01:05Z
date_published: 2023-05-01T00:00:00Z
date_updated: 2023-10-04T10:21:07Z
day: '01'
department:
- _id: LaEr
doi: 10.3150/22-BEJ1490
ec_funded: 1
external_id:
  arxiv:
  - '2112.12093 '
  isi:
  - '000947270100008'
intvolume: '        29'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2112.12093
month: '05'
oa: 1
oa_version: Preprint
page: 1063-1079
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Bernoulli
publication_identifier:
  issn:
  - 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
scopus_import: '1'
status: public
title: Small deviation estimates for the largest eigenvalue of Wigner matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 29
year: '2023'
...
---
_id: '12281'
abstract:
- lang: eng
  text: We study the hydrodynamic and hydrostatic limits of the one-dimensional open
    symmetric inclusion process with slow boundary. Depending on the value of the
    parameter tuning the interaction rate of the bulk of the system with the boundary,
    we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary
    conditions as hydrodynamic equation. In our approach, we combine duality and first-second
    class particle techniques to reduce the scaling limit of the inclusion process
    to the limiting behavior of a single, non-interacting, particle.
acknowledgement: "C.F. and P.G. thank FCT/Portugal for support through the project
  UID/MAT/04459/2013.\r\nThis project has received funding from the European Research
  Council (ERC) under the European Union’s Horizon 2020 research and innovative programme
  (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020
  research and innovation programme under the Marie-Skłodowska-Curie grant agreement
  No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at
  an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this
  work has been done, and the European research and innovative programme No. 715734
  for the kind hospitality."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
  full_name: Franceschini, Chiara
  last_name: Franceschini
- first_name: Patrícia
  full_name: Gonçalves, Patrícia
  last_name: Gonçalves
- first_name: Federico
  full_name: Sau, Federico
  id: E1836206-9F16-11E9-8814-AEFDE5697425
  last_name: Sau
citation:
  ama: 'Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow
    boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>. 2022;28(2):1340-1381.
    doi:<a href="https://doi.org/10.3150/21-bej1390">10.3150/21-bej1390</a>'
  apa: 'Franceschini, C., Gonçalves, P., &#38; Sau, F. (2022). Symmetric inclusion
    process with slow boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>.
    Bernoulli Society for Mathematical Statistics and Probability. <a href="https://doi.org/10.3150/21-bej1390">https://doi.org/10.3150/21-bej1390</a>'
  chicago: 'Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric
    Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>.
    Bernoulli Society for Mathematical Statistics and Probability, 2022. <a href="https://doi.org/10.3150/21-bej1390">https://doi.org/10.3150/21-bej1390</a>.'
  ieee: 'C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with
    slow boundary: Hydrodynamics and hydrostatics,” <i>Bernoulli</i>, vol. 28, no.
    2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381,
    2022.'
  ista: 'Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with
    slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.'
  mla: 'Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary:
    Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>, vol. 28, no. 2, Bernoulli Society
    for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:<a href="https://doi.org/10.3150/21-bej1390">10.3150/21-bej1390</a>.'
  short: C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.
date_created: 2023-01-16T10:03:04Z
date_published: 2022-05-01T00:00:00Z
date_updated: 2023-08-04T10:27:35Z
day: '01'
department:
- _id: JaMa
doi: 10.3150/21-bej1390
ec_funded: 1
external_id:
  arxiv:
  - '2007.11998'
  isi:
  - '000766619100025'
intvolume: '        28'
isi: 1
issue: '2'
keyword:
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2007.11998
month: '05'
oa: 1
oa_version: Preprint
page: 1340-1381
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Bernoulli
publication_identifier:
  issn:
  - 1350-7265
publication_status: published
publisher: Bernoulli Society for Mathematical Statistics and Probability
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics'
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 28
year: '2022'
...