---
_id: '6232'
abstract:
- lang: eng
  text: 'The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary
    conditions can be surprisingly—and in a sense, arbitrarily—bad: as shown by Krylov[
    SIAM J. Math. Anal.34(2003) 1167–1182], for any α>0 one can find a simple 1-dimensional
    constant coefficient linear equation whose solution at the boundary is not α-Hölder
    continuous.We obtain a positive counterpart of this: under some mild regularity
    assumptions on the coefficients, solutions of semilinear SPDEs on C1 domains are
    proved to be α-Hölder continuous up to the boundary with some α>0.'
article_processing_charge: No
arxiv: 1
author:
- first_name: Mate
  full_name: Gerencser, Mate
  id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
  last_name: Gerencser
citation:
  ama: Gerencser M. Boundary regularity of stochastic PDEs. <i>Annals of Probability</i>.
    2019;47(2):804-834. doi:<a href="https://doi.org/10.1214/18-AOP1272">10.1214/18-AOP1272</a>
  apa: Gerencser, M. (2019). Boundary regularity of stochastic PDEs. <i>Annals of
    Probability</i>. Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/18-AOP1272">https://doi.org/10.1214/18-AOP1272</a>
  chicago: Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” <i>Annals of
    Probability</i>. Institute of Mathematical Statistics, 2019. <a href="https://doi.org/10.1214/18-AOP1272">https://doi.org/10.1214/18-AOP1272</a>.
  ieee: M. Gerencser, “Boundary regularity of stochastic PDEs,” <i>Annals of Probability</i>,
    vol. 47, no. 2. Institute of Mathematical Statistics, pp. 804–834, 2019.
  ista: Gerencser M. 2019. Boundary regularity of stochastic PDEs. Annals of Probability.
    47(2), 804–834.
  mla: Gerencser, Mate. “Boundary Regularity of Stochastic PDEs.” <i>Annals of Probability</i>,
    vol. 47, no. 2, Institute of Mathematical Statistics, 2019, pp. 804–34, doi:<a
    href="https://doi.org/10.1214/18-AOP1272">10.1214/18-AOP1272</a>.
  short: M. Gerencser, Annals of Probability 47 (2019) 804–834.
date_created: 2019-04-07T21:59:15Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-08-25T08:59:11Z
day: '01'
department:
- _id: JaMa
doi: 10.1214/18-AOP1272
external_id:
  arxiv:
  - '1705.05364'
  isi:
  - '000459681900005'
intvolume: '        47'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1705.05364
month: '03'
oa: 1
oa_version: Preprint
page: 804-834
publication: Annals of Probability
publication_identifier:
  issn:
  - '00911798'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Boundary regularity of stochastic PDEs
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2019'
...
---
_id: '6511'
abstract:
- lang: eng
  text: Let U and V be two independent N by N random matrices that are distributed
    according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N
    matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts
    that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly,
    in the limit of large N, to a deterministic measure which is supported on a single
    ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior
    of the single ring, we establish the convergence of the empirical eigenvalue distribution
    on the optimal local scale of order N−1/2+ε and establish the optimal convergence
    rate. The same results hold true when U and V are Haar distributed on O(N).
article_processing_charge: No
arxiv: 1
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 single ring theorem on optimal scale. <i>Annals
    of Probability</i>. 2019;47(3):1270-1334. doi:<a href="https://doi.org/10.1214/18-AOP1284">10.1214/18-AOP1284</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on
    optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics.
    <a href="https://doi.org/10.1214/18-AOP1284">https://doi.org/10.1214/18-AOP1284</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem
    on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics,
    2019. <a href="https://doi.org/10.1214/18-AOP1284">https://doi.org/10.1214/18-AOP1284</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,”
    <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics,
    pp. 1270–1334, 2019.
  ista: Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale.
    Annals of Probability. 47(3), 1270–1334.
  mla: Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals
    of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019,
    pp. 1270–334, doi:<a href="https://doi.org/10.1214/18-AOP1284">10.1214/18-AOP1284</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.
date_created: 2019-06-02T21:59:13Z
date_published: 2019-05-01T00:00:00Z
date_updated: 2023-08-28T09:32:29Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/18-AOP1284
ec_funded: 1
external_id:
  arxiv:
  - '1612.05920'
  isi:
  - '000466616100003'
intvolume: '        47'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1612.05920
month: '05'
oa: 1
oa_version: Preprint
page: 1270-1334
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Annals of Probability
publication_identifier:
  issn:
  - '00911798'
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local single ring theorem on optimal scale
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2019'
...