---
_id: '8601'
abstract:
- lang: eng
  text: We consider large non-Hermitian real or complex random matrices X with independent,
    identically distributed centred entries. We prove that their local eigenvalue
    statistics near the spectral edge, the unit circle, coincide with those of the
    Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result
    is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution
    at the spectral edges of the Wigner ensemble.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
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. Edge universality for non-Hermitian random
    matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href="https://doi.org/10.1007/s00440-020-01003-7">10.1007/s00440-020-01003-7</a>
  apa: Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Edge universality for
    non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00440-020-01003-7">https://doi.org/10.1007/s00440-020-01003-7</a>
  chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality
    for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1007/s00440-020-01003-7">https://doi.org/10.1007/s00440-020-01003-7</a>.
  ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian
    random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature,
    2021.
  ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian
    random matrices. Probability Theory and Related Fields.
  mla: Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.”
    <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s00440-020-01003-7">10.1007/s00440-020-01003-7</a>.
  short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields
    (2021).
date_created: 2020-10-04T22:01:37Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2024-03-07T15:07:53Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-020-01003-7
ec_funded: 1
external_id:
  arxiv:
  - '1908.00969'
  isi:
  - '000572724600002'
file:
- access_level: open_access
  checksum: 611ae28d6055e1e298d53a57beb05ef4
  content_type: application/pdf
  creator: dernst
  date_created: 2020-10-05T14:53:40Z
  date_updated: 2020-10-05T14:53:40Z
  file_id: '8612'
  file_name: 2020_ProbTheory_Cipolloni.pdf
  file_size: 497032
  relation: main_file
  success: 1
file_date_updated: 2020-10-05T14:53:40Z
has_accepted_license: '1'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '665385'
  name: International IST Doctoral Program
publication: Probability Theory and Related Fields
publication_identifier:
  eissn:
  - '14322064'
  issn:
  - '01788051'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Edge universality for non-Hermitian 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: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '319'
abstract:
- lang: eng
  text: We study spaces of modelled distributions with singular behaviour near the
    boundary of a domain that, in the context of the theory of regularity structures,
    allow one to give robust solution theories for singular stochastic PDEs with boundary
    conditions. The calculus of modelled distributions established in Hairer (Invent
    Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended
    to this setting. We formulate and solve fixed point problems in these spaces with
    a class of kernels that is sufficiently large to cover in particular the Dirichlet
    and Neumann heat kernels. These results are then used to provide solution theories
    for the KPZ equation with Dirichlet and Neumann boundary conditions and for the
    2D generalised parabolic Anderson model with Dirichlet boundary conditions. In
    the case of the KPZ equation with Neumann boundary conditions, we show that, depending
    on the class of mollifiers one considers, a “boundary renormalisation” takes place.
    In other words, there are situations in which a certain boundary condition is
    applied to an approximation to the KPZ equation, but the limiting process is the
    Hopf–Cole solution to the KPZ equation with a different boundary condition.
acknowledgement: "MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Mate
  full_name: Gerencser, Mate
  id: 44ECEDF2-F248-11E8-B48F-1D18A9856A87
  last_name: Gerencser
- first_name: Martin
  full_name: Hairer, Martin
  last_name: Hairer
citation:
  ama: Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. <i>Probability
    Theory and Related Fields</i>. 2019;173(3-4):697–758. doi:<a href="https://doi.org/10.1007/s00440-018-0841-1">10.1007/s00440-018-0841-1</a>
  apa: Gerencser, M., &#38; Hairer, M. (2019). Singular SPDEs in domains with boundaries.
    <i>Probability Theory and Related Fields</i>. Springer. <a href="https://doi.org/10.1007/s00440-018-0841-1">https://doi.org/10.1007/s00440-018-0841-1</a>
  chicago: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
    <i>Probability Theory and Related Fields</i>. Springer, 2019. <a href="https://doi.org/10.1007/s00440-018-0841-1">https://doi.org/10.1007/s00440-018-0841-1</a>.
  ieee: M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” <i>Probability
    Theory and Related Fields</i>, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.
  ista: Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability
    Theory and Related Fields. 173(3–4), 697–758.
  mla: Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.”
    <i>Probability Theory and Related Fields</i>, vol. 173, no. 3–4, Springer, 2019,
    pp. 697–758, doi:<a href="https://doi.org/10.1007/s00440-018-0841-1">10.1007/s00440-018-0841-1</a>.
  short: M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019)
    697–758.
date_created: 2018-12-11T11:45:48Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2023-08-24T14:38:32Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00440-018-0841-1
external_id:
  isi:
  - '000463613800001'
file:
- access_level: open_access
  checksum: 288d16ef7291242f485a9660979486e3
  content_type: application/pdf
  creator: dernst
  date_created: 2018-12-17T16:25:24Z
  date_updated: 2020-07-14T12:46:03Z
  file_id: '5722'
  file_name: 2018_ProbTheory_Gerencser.pdf
  file_size: 893182
  relation: main_file
file_date_updated: 2020-07-14T12:46:03Z
has_accepted_license: '1'
intvolume: '       173'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 697–758
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
  eissn:
  - '14322064'
  issn:
  - '01788051'
publication_status: published
publisher: Springer
publist_id: '7546'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Singular SPDEs in domains with boundaries
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: 173
year: '2019'
...
---
_id: '429'
abstract:
- lang: eng
  text: We consider real symmetric or complex hermitian random matrices with correlated
    entries. We prove local laws for the resolvent and universality of the local eigenvalue
    statistics in the bulk of the spectrum. The correlations have fast decay but are
    otherwise of general form. The key novelty is the detailed stability analysis
    of the corresponding matrix valued Dyson equation whose solution is the deterministic
    limit of the resolvent.
acknowledgement: "Open access funding provided by Institute of Science and Technology
  (IST Austria).\r\n"
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Oskari H
  full_name: Ajanki, Oskari H
  id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
  last_name: Ajanki
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
citation:
  ama: Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random
    matrices with correlations. <i>Probability Theory and Related Fields</i>. 2019;173(1-2):293–373.
    doi:<a href="https://doi.org/10.1007/s00440-018-0835-z">10.1007/s00440-018-0835-z</a>
  apa: Ajanki, O. H., Erdös, L., &#38; Krüger, T. H. (2019). Stability of the matrix
    Dyson equation and random matrices with correlations. <i>Probability Theory and
    Related Fields</i>. Springer. <a href="https://doi.org/10.1007/s00440-018-0835-z">https://doi.org/10.1007/s00440-018-0835-z</a>
  chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the
    Matrix Dyson Equation and Random Matrices with Correlations.” <i>Probability Theory
    and Related Fields</i>. Springer, 2019. <a href="https://doi.org/10.1007/s00440-018-0835-z">https://doi.org/10.1007/s00440-018-0835-z</a>.
  ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation
    and random matrices with correlations,” <i>Probability Theory and Related Fields</i>,
    vol. 173, no. 1–2. Springer, pp. 293–373, 2019.
  ista: Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation
    and random matrices with correlations. Probability Theory and Related Fields.
    173(1–2), 293–373.
  mla: Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random
    Matrices with Correlations.” <i>Probability Theory and Related Fields</i>, vol.
    173, no. 1–2, Springer, 2019, pp. 293–373, doi:<a href="https://doi.org/10.1007/s00440-018-0835-z">10.1007/s00440-018-0835-z</a>.
  short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
    173 (2019) 293–373.
date_created: 2018-12-11T11:46:25Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2023-08-24T14:39:00Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1007/s00440-018-0835-z
ec_funded: 1
external_id:
  isi:
  - '000459396500007'
file:
- access_level: open_access
  checksum: f9354fa5c71f9edd17132588f0dc7d01
  content_type: application/pdf
  creator: dernst
  date_created: 2018-12-17T16:12:08Z
  date_updated: 2020-07-14T12:46:26Z
  file_id: '5720'
  file_name: 2018_ProbTheory_Ajanki.pdf
  file_size: 1201840
  relation: main_file
file_date_updated: 2020-07-14T12:46:26Z
has_accepted_license: '1'
intvolume: '       173'
isi: 1
issue: 1-2
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 293–373
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Probability Theory and Related Fields
publication_identifier:
  eissn:
  - '14322064'
  issn:
  - '01788051'
publication_status: published
publisher: Springer
publist_id: '7394'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Stability of the matrix Dyson equation and random matrices with correlations
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: 173
year: '2019'
...
---
_id: '1528'
abstract:
- lang: eng
  text: 'We consider N×N Hermitian random matrices H consisting of blocks of size
    M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian
    in the four moment matching sense, but their distribution varies from block to
    block to form a block-band structure, with an essential band width M. We show
    that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle
    law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using
    a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys
    155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous
    estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors
    in the middle of the spectrum are fully delocalized.'
acknowledgement: "Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L.
  Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access
  funding provided by Institute of Science and Technology (IST Austria). The authors
  are very grateful to the anonymous referees for careful reading and valuable comments,
  which helped to improve the organization."
article_processing_charge: Yes (via OA deal)
article_type: original
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
citation:
  ama: Bao Z, Erdös L. Delocalization for a class of random block band matrices. <i>Probability
    Theory and Related Fields</i>. 2017;167(3-4):673-776. doi:<a href="https://doi.org/10.1007/s00440-015-0692-y">10.1007/s00440-015-0692-y</a>
  apa: Bao, Z., &#38; Erdös, L. (2017). Delocalization for a class of random block
    band matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href="https://doi.org/10.1007/s00440-015-0692-y">https://doi.org/10.1007/s00440-015-0692-y</a>
  chicago: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
    Band Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2017.
    <a href="https://doi.org/10.1007/s00440-015-0692-y">https://doi.org/10.1007/s00440-015-0692-y</a>.
  ieee: Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,”
    <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4. Springer, pp.
    673–776, 2017.
  ista: Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices.
    Probability Theory and Related Fields. 167(3–4), 673–776.
  mla: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block
    Band Matrices.” <i>Probability Theory and Related Fields</i>, vol. 167, no. 3–4,
    Springer, 2017, pp. 673–776, doi:<a href="https://doi.org/10.1007/s00440-015-0692-y">10.1007/s00440-015-0692-y</a>.
  short: Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.
date_created: 2018-12-11T11:52:32Z
date_published: 2017-04-01T00:00:00Z
date_updated: 2023-09-20T09:42:12Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00440-015-0692-y
ec_funded: 1
external_id:
  isi:
  - '000398842700004'
file:
- access_level: open_access
  checksum: 67afa85ff1e220cbc1f9f477a828513c
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:08:05Z
  date_updated: 2020-07-14T12:45:00Z
  file_id: '4665'
  file_name: IST-2016-489-v1+1_s00440-015-0692-y.pdf
  file_size: 1615755
  relation: main_file
file_date_updated: 2020-07-14T12:45:00Z
has_accepted_license: '1'
intvolume: '       167'
isi: 1
issue: 3-4
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 673 - 776
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Probability Theory and Related Fields
publication_identifier:
  issn:
  - '01788051'
publication_status: published
publisher: Springer
publist_id: '5644'
pubrep_id: '489'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Delocalization for a class of random block band 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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 167
year: '2017'
...
---
_id: '1337'
abstract:
- lang: eng
  text: We consider the local eigenvalue distribution of large self-adjoint N×N random
    matrices H=H∗ with centered independent entries. In contrast to previous works
    the matrix of variances sij=\mathbbmE|hij|2 is not assumed to be stochastic. Hence
    the density of states is not the Wigner semicircle law. Its possible shapes are
    described in the companion paper (Ajanki et al. in Quadratic Vector Equations
    on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the
    resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z))
    solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki
    et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095).
    We prove a local law down to the smallest spectral resolution scale, and bulk
    universality for both real symmetric and complex hermitian symmetry classes.
acknowledgement: 'Open access funding provided by Institute of Science and Technology
  (IST Austria).  '
article_processing_charge: Yes (via OA deal)
author:
- first_name: Oskari H
  full_name: Ajanki, Oskari H
  id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87
  last_name: Ajanki
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Torben H
  full_name: Krüger, Torben H
  id: 3020C786-F248-11E8-B48F-1D18A9856A87
  last_name: Krüger
  orcid: 0000-0002-4821-3297
citation:
  ama: Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices.
    <i>Probability Theory and Related Fields</i>. 2017;169(3-4):667-727. doi:<a href="https://doi.org/10.1007/s00440-016-0740-2">10.1007/s00440-016-0740-2</a>
  apa: Ajanki, O. H., Erdös, L., &#38; Krüger, T. H. (2017). Universality for general
    Wigner-type matrices. <i>Probability Theory and Related Fields</i>. Springer.
    <a href="https://doi.org/10.1007/s00440-016-0740-2">https://doi.org/10.1007/s00440-016-0740-2</a>
  chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for
    General Wigner-Type Matrices.” <i>Probability Theory and Related Fields</i>. Springer,
    2017. <a href="https://doi.org/10.1007/s00440-016-0740-2">https://doi.org/10.1007/s00440-016-0740-2</a>.
  ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type
    matrices,” <i>Probability Theory and Related Fields</i>, vol. 169, no. 3–4. Springer,
    pp. 667–727, 2017.
  ista: Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type
    matrices. Probability Theory and Related Fields. 169(3–4), 667–727.
  mla: Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.”
    <i>Probability Theory and Related Fields</i>, vol. 169, no. 3–4, Springer, 2017,
    pp. 667–727, doi:<a href="https://doi.org/10.1007/s00440-016-0740-2">10.1007/s00440-016-0740-2</a>.
  short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields
    169 (2017) 667–727.
date_created: 2018-12-11T11:51:27Z
date_published: 2017-12-01T00:00:00Z
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doi: 10.1007/s00440-016-0740-2
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publication: Probability Theory and Related Fields
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publisher: Springer
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title: Universality for general Wigner-type matrices
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...