---
_id: '12290'
abstract:
- lang: eng
  text: We prove local laws, i.e. optimal concentration estimates for arbitrary products
    of resolvents of a Wigner random matrix with deterministic matrices in between.
    We find that the size of such products heavily depends on whether some of the
    deterministic matrices are traceless. Our estimates correctly account for this
    dependence and they hold optimally down to the smallest possible spectral scale.
acknowledgement: L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.
  D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and
  the ETH Zürich Foundation.
article_processing_charge: No
article_type: original
author:
- first_name: Giorgio
  full_name: Cipolloni, Giorgio
  id: 42198EFA-F248-11E8-B48F-1D18A9856A87
  last_name: Cipolloni
  orcid: 0000-0002-4901-7992
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- 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: Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner
    matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href="https://doi.org/10.1214/22-ejp838">10.1214/22-ejp838</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent
    local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute
    of Mathematical Statistics. <a href="https://doi.org/10.1214/22-ejp838">https://doi.org/10.1214/22-ejp838</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent
    Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute
    of Mathematical Statistics, 2022. <a href="https://doi.org/10.1214/22-ejp838">https://doi.org/10.1214/22-ejp838</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local
    laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27.
    Institute of Mathematical Statistics, pp. 1–38, 2022.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws
    for Wigner matrices. Electronic Journal of Probability. 27, 1–38.
  mla: Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.”
    <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics,
    2022, pp. 1–38, doi:<a href="https://doi.org/10.1214/22-ejp838">10.1214/22-ejp838</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability
    27 (2022) 1–38.
date_created: 2023-01-16T10:04:38Z
date_published: 2022-09-12T00:00:00Z
date_updated: 2023-08-04T10:32:23Z
day: '12'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/22-ejp838
ec_funded: 1
external_id:
  isi:
  - '000910863700003'
file:
- access_level: open_access
  checksum: bb647b48fbdb59361210e425c220cdcb
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-30T11:59:21Z
  date_updated: 2023-01-30T11:59:21Z
  file_id: '12464'
  file_name: 2022_ElecJournProbability_Cipolloni.pdf
  file_size: 502149
  relation: main_file
  success: 1
file_date_updated: 2023-01-30T11:59:21Z
has_accepted_license: '1'
intvolume: '        27'
isi: 1
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1-38
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Journal of Probability
publication_identifier:
  eissn:
  - 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal multi-resolvent local laws for Wigner 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2022'
...
---
_id: '10285'
abstract:
- lang: eng
  text: We study the overlaps between right and left eigenvectors for random matrices
    of the spherical ensemble, as well as truncated unitary ensembles in the regime
    where half of the matrix at least is truncated. These two integrable models exhibit
    a form of duality, and the essential steps of our investigation can therefore
    be performed in parallel. In every case, conditionally on all eigenvalues, diagonal
    overlaps are shown to be distributed as a product of independent random variables
    with explicit distributions. This enables us to prove that the scaled diagonal
    overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail
    limit, namely, the inverse of a γ2 distribution. We also provide formulae for
    the conditional expectation of diagonal and off-diagonal overlaps, either with
    respect to one eigenvalue, or with respect to the whole spectrum. These results,
    analogous to what is known for the complex Ginibre ensemble, can be obtained in
    these cases thanks to integration techniques inspired from a previous work by
    Forrester & Krishnapur.
acknowledgement: We acknowledge partial support from the grants NSF DMS-1812114 of
  P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has
  also received funding from the European Union’s Horizon 2020 research and innovation
  programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would
  like to thank Paul Bourgade and László Erdős for many helpful comments.
article_number: '124'
article_processing_charge: No
article_type: original
author:
- first_name: Guillaume
  full_name: Dubach, Guillaume
  id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
  last_name: Dubach
  orcid: 0000-0001-6892-8137
citation:
  ama: Dubach G. On eigenvector statistics in the spherical and truncated unitary
    ensembles. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href="https://doi.org/10.1214/21-EJP686">10.1214/21-EJP686</a>
  apa: Dubach, G. (2021). On eigenvector statistics in the spherical and truncated
    unitary ensembles. <i>Electronic Journal of Probability</i>. Institute of Mathematical
    Statistics. <a href="https://doi.org/10.1214/21-EJP686">https://doi.org/10.1214/21-EJP686</a>
  chicago: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
    Unitary Ensembles.” <i>Electronic Journal of Probability</i>. Institute of Mathematical
    Statistics, 2021. <a href="https://doi.org/10.1214/21-EJP686">https://doi.org/10.1214/21-EJP686</a>.
  ieee: G. Dubach, “On eigenvector statistics in the spherical and truncated unitary
    ensembles,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical
    Statistics, 2021.
  ista: Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary
    ensembles. Electronic Journal of Probability. 26, 124.
  mla: Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated
    Unitary Ensembles.” <i>Electronic Journal of Probability</i>, vol. 26, 124, Institute
    of Mathematical Statistics, 2021, doi:<a href="https://doi.org/10.1214/21-EJP686">10.1214/21-EJP686</a>.
  short: G. Dubach, Electronic Journal of Probability 26 (2021).
date_created: 2021-11-14T23:01:25Z
date_published: 2021-09-28T00:00:00Z
date_updated: 2021-11-15T10:48:46Z
day: '28'
ddc:
- '519'
department:
- _id: LaEr
doi: 10.1214/21-EJP686
ec_funded: 1
file:
- access_level: open_access
  checksum: 1c975afb31460277ce4d22b93538e5f9
  content_type: application/pdf
  creator: cchlebak
  date_created: 2021-11-15T10:10:17Z
  date_updated: 2021-11-15T10:10:17Z
  file_id: '10288'
  file_name: 2021_ElecJournalProb_Dubach.pdf
  file_size: 735940
  relation: main_file
  success: 1
file_date_updated: 2021-11-15T10:10:17Z
has_accepted_license: '1'
intvolume: '        26'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
  eissn:
  - 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On eigenvector statistics in the spherical and truncated unitary ensembles
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: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 26
year: '2021'
...
---
_id: '8973'
abstract:
- lang: eng
  text: We consider the symmetric simple exclusion process in Zd with quenched bounded
    dynamic random conductances and prove its hydrodynamic limit in path space. The
    main tool is the connection, due to the self-duality of the process, between the
    invariance principle for single particles starting from all points and the macroscopic
    behavior of the density field. While the hydrodynamic limit at fixed macroscopic
    times is obtained via a generalization to the time-inhomogeneous context of the
    strategy introduced in [41], in order to prove tightness for the sequence of empirical
    density fields we develop a new criterion based on the notion of uniform conditional
    stochastic continuity, following [50]. In conclusion, we show that uniform elliptic
    dynamic conductances provide an example of environments in which the so-called
    arbitrary starting point invariance principle may be derived from the invariance
    principle of a single particle starting from the origin. Therefore, our hydrodynamics
    result applies to the examples of quenched environments considered in, e.g., [1],
    [3], [6] in combination with the hypothesis of uniform ellipticity.
acknowledgement: "We warmly thank S.R.S. Varadhan for many enlightening discussions
  at an early stage of this work. We are indebted to Francesca Collet for fruitful
  discussions and constant support all throughout this work. We thank Simone Floreani\r\nand
  Alberto Chiarini for helpful conversations on the final part of this paper as well
  as both referees for their careful reading and for raising relevant issues on some
  weak points contained in a previous version of this manuscript; we believe this
  helped us to improve it.\r\nPart of this work was done during the authors’ stay
  at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile
  Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank
  this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01).
  F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University,
  for financial support and hospitality. F.S. acknowledges NWO for financial support
  via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon
  2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement
  No. 754411. This research has been conducted within the FP2M federation (CNRS FR
  2036)."
article_number: '138'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Frank
  full_name: Redig, Frank
  last_name: Redig
- first_name: Ellen
  full_name: Saada, Ellen
  last_name: Saada
- first_name: Federico
  full_name: Sau, Federico
  id: E1836206-9F16-11E9-8814-AEFDE5697425
  last_name: Sau
citation:
  ama: 'Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment:
    Hydrodynamics. <i>Electronic Journal of Probability</i>. 2020;25. doi:<a href="https://doi.org/10.1214/20-EJP536">10.1214/20-EJP536</a>'
  apa: 'Redig, F., Saada, E., &#38; Sau, F. (2020). Symmetric simple exclusion process
    in dynamic environment: Hydrodynamics. <i>Electronic Journal of Probability</i>.  Institute
    of Mathematical Statistics. <a href="https://doi.org/10.1214/20-EJP536">https://doi.org/10.1214/20-EJP536</a>'
  chicago: 'Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion
    Process in Dynamic Environment: Hydrodynamics.” <i>Electronic Journal of Probability</i>.  Institute
    of Mathematical Statistics, 2020. <a href="https://doi.org/10.1214/20-EJP536">https://doi.org/10.1214/20-EJP536</a>.'
  ieee: 'F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic
    environment: Hydrodynamics,” <i>Electronic Journal of Probability</i>, vol. 25.  Institute
    of Mathematical Statistics, 2020.'
  ista: 'Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic
    environment: Hydrodynamics. Electronic Journal of Probability. 25, 138.'
  mla: 'Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment:
    Hydrodynamics.” <i>Electronic Journal of Probability</i>, vol. 25, 138,  Institute
    of Mathematical Statistics, 2020, doi:<a href="https://doi.org/10.1214/20-EJP536">10.1214/20-EJP536</a>.'
  short: F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).
date_created: 2020-12-27T23:01:17Z
date_published: 2020-10-21T00:00:00Z
date_updated: 2023-10-17T12:51:56Z
day: '21'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/20-EJP536
ec_funded: 1
external_id:
  arxiv:
  - '1811.01366'
  isi:
  - '000591737500001'
file:
- access_level: open_access
  checksum: d75359b9814e78d57c0a481b7cde3751
  content_type: application/pdf
  creator: dernst
  date_created: 2020-12-28T08:24:08Z
  date_updated: 2020-12-28T08:24:08Z
  file_id: '8976'
  file_name: 2020_ElectronJProbab_Redig.pdf
  file_size: 696653
  relation: main_file
  success: 1
file_date_updated: 2020-12-28T08:24:08Z
has_accepted_license: '1'
intvolume: '        25'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
publication: Electronic Journal of Probability
publication_identifier:
  eissn:
  - 1083-6489
publication_status: published
publisher: ' Institute of Mathematical Statistics'
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Symmetric simple exclusion process in dynamic environment: Hydrodynamics'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2020'
...
---
_id: '6359'
abstract:
- lang: eng
  text: The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate
    SDEs with irregular drift coefficients is considered. In the case of α-Hölder
    drift in the recent literature the rate α/2 was proved in many related situations.
    By exploiting the regularising effect of the noise more efficiently, we show that
    the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to
    Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.
article_number: '82'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Konstantinos
  full_name: Dareiotis, Konstantinos
  last_name: Dareiotis
- first_name: Mate
  full_name: Gerencser, Mate
  id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
  last_name: Gerencser
citation:
  ama: Dareiotis K, Gerencser M. On the regularisation of the noise for the Euler-Maruyama
    scheme with irregular drift. <i>Electronic Journal of Probability</i>. 2020;25.
    doi:<a href="https://doi.org/10.1214/20-EJP479">10.1214/20-EJP479</a>
  apa: Dareiotis, K., &#38; Gerencser, M. (2020). On the regularisation of the noise
    for the Euler-Maruyama scheme with irregular drift. <i>Electronic Journal of Probability</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/20-EJP479">https://doi.org/10.1214/20-EJP479</a>
  chicago: Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of
    the Noise for the Euler-Maruyama Scheme with Irregular Drift.” <i>Electronic Journal
    of Probability</i>. Institute of Mathematical Statistics, 2020. <a href="https://doi.org/10.1214/20-EJP479">https://doi.org/10.1214/20-EJP479</a>.
  ieee: K. Dareiotis and M. Gerencser, “On the regularisation of the noise for the
    Euler-Maruyama scheme with irregular drift,” <i>Electronic Journal of Probability</i>,
    vol. 25. Institute of Mathematical Statistics, 2020.
  ista: Dareiotis K, Gerencser M. 2020. On the regularisation of the noise for the
    Euler-Maruyama scheme with irregular drift. Electronic Journal of Probability.
    25, 82.
  mla: Dareiotis, Konstantinos, and Mate Gerencser. “On the Regularisation of the
    Noise for the Euler-Maruyama Scheme with Irregular Drift.” <i>Electronic Journal
    of Probability</i>, vol. 25, 82, Institute of Mathematical Statistics, 2020, doi:<a
    href="https://doi.org/10.1214/20-EJP479">10.1214/20-EJP479</a>.
  short: K. Dareiotis, M. Gerencser, Electronic Journal of Probability 25 (2020).
date_created: 2019-04-30T07:40:17Z
date_published: 2020-07-16T00:00:00Z
date_updated: 2023-10-16T09:22:50Z
day: '16'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/20-EJP479
external_id:
  arxiv:
  - '1812.04583'
  isi:
  - '000550150700001'
file:
- access_level: open_access
  checksum: 8e7c42e72596f6889d786e8e8b89994f
  content_type: application/pdf
  creator: dernst
  date_created: 2020-09-21T13:15:02Z
  date_updated: 2020-09-21T13:15:02Z
  file_id: '8549'
  file_name: 2020_EJournProbab_Dareiotis.pdf
  file_size: 273042
  relation: main_file
  success: 1
file_date_updated: 2020-09-21T13:15:02Z
has_accepted_license: '1'
intvolume: '        25'
isi: 1
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
publication: Electronic Journal of Probability
publication_identifier:
  eissn:
  - 1083-6489
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the regularisation of the noise for the Euler-Maruyama scheme with irregular
  drift
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: 25
year: '2020'
...