---
OA_place: repository
OA_type: green
_id: '18880'
abstract:
- lang: eng
  text: In this paper, we provide a rate of convergence for a version of the Carathéodory
    convergence for the multiple SLE model with a Dyson Brownian motion driver towards
    its hydrodynamic limit, for β=1 and β=2. The results are obtained by combining
    techniques from the field of Schramm–Loewner Evolutions with modern techniques
    from random matrices. Our approach shows how one can apply modern tools used in
    the proof of universality in random matrix theory to the field of Schramm–Loewner
    Evolutions.
article_number: '2450028'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Andrew J
  full_name: Campbell, Andrew J
  id: 582b06a9-1f1c-11ee-b076-82ffce00dde4
  last_name: Campbell
- first_name: Kyle
  full_name: Luh, Kyle
  last_name: Luh
- first_name: Vlad
  full_name: Margarint, Vlad
  last_name: Margarint
citation:
  ama: 'Campbell AJ, Luh K, Margarint V. Rate of convergence in multiple SLE using
    random matrix theory. <i>Random Matrices: Theory and Application</i>. 2025;14(1).
    doi:<a href="https://doi.org/10.1142/S201032632450028X">10.1142/S201032632450028X</a>'
  apa: 'Campbell, A. J., Luh, K., &#38; Margarint, V. (2025). Rate of convergence
    in multiple SLE using random matrix theory. <i>Random Matrices: Theory and Application</i>.
    World Scientific Publishing. <a href="https://doi.org/10.1142/S201032632450028X">https://doi.org/10.1142/S201032632450028X</a>'
  chicago: 'Campbell, Andrew J, Kyle Luh, and Vlad Margarint. “Rate of Convergence
    in Multiple SLE Using Random Matrix Theory.” <i>Random Matrices: Theory and Application</i>.
    World Scientific Publishing, 2025. <a href="https://doi.org/10.1142/S201032632450028X">https://doi.org/10.1142/S201032632450028X</a>.'
  ieee: 'A. J. Campbell, K. Luh, and V. Margarint, “Rate of convergence in multiple
    SLE using random matrix theory,” <i>Random Matrices: Theory and Application</i>,
    vol. 14, no. 1. World Scientific Publishing, 2025.'
  ista: 'Campbell AJ, Luh K, Margarint V. 2025. Rate of convergence in multiple SLE
    using random matrix theory. Random Matrices: Theory and Application. 14(1), 2450028.'
  mla: 'Campbell, Andrew J., et al. “Rate of Convergence in Multiple SLE Using Random
    Matrix Theory.” <i>Random Matrices: Theory and Application</i>, vol. 14, no. 1,
    2450028, World Scientific Publishing, 2025, doi:<a href="https://doi.org/10.1142/S201032632450028X">10.1142/S201032632450028X</a>.'
  short: 'A.J. Campbell, K. Luh, V. Margarint, Random Matrices: Theory and Application
    14 (2025).'
date_created: 2025-01-26T23:01:49Z
date_published: 2025-01-01T00:00:00Z
date_updated: 2025-07-10T11:51:29Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S201032632450028X
external_id:
  arxiv:
  - '2301.04722'
  isi:
  - '001397136000001'
intvolume: '        14'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2301.04722
month: '01'
oa: 1
oa_version: Preprint
publication: 'Random Matrices: Theory and Application'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rate of convergence in multiple SLE using random matrix theory
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '17047'
abstract:
- lang: eng
  text: We provide a dynamical study of a model of multiplicative perturbation of
    a unitary matrix introduced by Fyodorov. In particular, we identify a flow of
    deterministic domains that bound the spectrum with high probability, separating
    the outlier from the typical eigenvalues at all sub-critical timescales. These
    results are obtained under generic assumptions on U that hold for a variety of
    unitary random matrix models.
article_number: '2450007'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guillaume
  full_name: Dubach, Guillaume
  id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
  last_name: Dubach
  orcid: 0000-0001-6892-8137
- first_name: Jana
  full_name: Reker, Jana
  id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
  last_name: Reker
citation:
  ama: 'Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a
    unitary matrix. <i>Random Matrices: Theory and Applications</i>. 2024;13(2). doi:<a
    href="https://doi.org/10.1142/s2010326324500072">10.1142/s2010326324500072</a>'
  apa: 'Dubach, G., &#38; Reker, J. (2024). Dynamics of a rank-one multiplicative
    perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>.
    World Scientific Publishing. <a href="https://doi.org/10.1142/s2010326324500072">https://doi.org/10.1142/s2010326324500072</a>'
  chicago: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative
    Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>.
    World Scientific Publishing, 2024. <a href="https://doi.org/10.1142/s2010326324500072">https://doi.org/10.1142/s2010326324500072</a>.'
  ieee: 'G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation
    of a unitary matrix,” <i>Random Matrices: Theory and Applications</i>, vol. 13,
    no. 2. World Scientific Publishing, 2024.'
  ista: 'Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation
    of a unitary matrix. Random Matrices: Theory and Applications. 13(2), 2450007.'
  mla: 'Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative
    Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>,
    vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:<a href="https://doi.org/10.1142/s2010326324500072">10.1142/s2010326324500072</a>.'
  short: 'G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).'
corr_author: '1'
date_created: 2024-05-23T08:31:57Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326324500072
ec_funded: 1
external_id:
  arxiv:
  - '2212.14638'
  isi:
  - '001229295200002'
intvolume: '        13'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2212.14638'
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
related_material:
  record:
  - id: '17164'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Dynamics of a rank-one multiplicative perturbation of a unitary matrix
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 13
year: '2024'
...
---
_id: '17079'
abstract:
- lang: eng
  text: We study moments of characteristic polynomials of truncated Haar distributed
    matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite
    matrix size we calculate the moments in terms of hypergeometric functions of matrix
    argument and give explicit integral representations highlighting the duality between
    the moment and the matrix size as well as the duality between the orthogonal and
    symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes
    are obtained. Using the connection to matrix hypergeometric functions, we establish
    limit theorems for the log-modulus of the characteristic polynomial evaluated
    on the unit circle.
acknowledgement: N.S. gratefully acknowledges financial support of the Royal Society,
  grant URF/R1/180707. We would like to thank Emma Bailey, Yan Fyodorov and Jordan
  Stoyanov for helpful comments an an earlier version of this paper. We are grateful
  for the comments of an anonymous referee.
article_number: '2250049'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Alexander
  full_name: Serebryakov, Alexander
  last_name: Serebryakov
- first_name: Nick
  full_name: Simm, Nick
  last_name: Simm
- first_name: Guillaume
  full_name: Dubach, Guillaume
  id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E
  last_name: Dubach
  orcid: 0000-0001-6892-8137
citation:
  ama: 'Serebryakov A, Simm N, Dubach G. Characteristic polynomials of random truncations:
    Moments, duality and asymptotics. <i>Random Matrices: Theory and Applications</i>.
    2023;12(01). doi:<a href="https://doi.org/10.1142/s2010326322500496">10.1142/s2010326322500496</a>'
  apa: 'Serebryakov, A., Simm, N., &#38; Dubach, G. (2023). Characteristic polynomials
    of random truncations: Moments, duality and asymptotics. <i>Random Matrices: Theory
    and Applications</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s2010326322500496">https://doi.org/10.1142/s2010326322500496</a>'
  chicago: 'Serebryakov, Alexander, Nick Simm, and Guillaume Dubach. “Characteristic
    Polynomials of Random Truncations: Moments, Duality and Asymptotics.” <i>Random
    Matrices: Theory and Applications</i>. World Scientific Publishing, 2023. <a href="https://doi.org/10.1142/s2010326322500496">https://doi.org/10.1142/s2010326322500496</a>.'
  ieee: 'A. Serebryakov, N. Simm, and G. Dubach, “Characteristic polynomials of random
    truncations: Moments, duality and asymptotics,” <i>Random Matrices: Theory and
    Applications</i>, vol. 12, no. 01. World Scientific Publishing, 2023.'
  ista: 'Serebryakov A, Simm N, Dubach G. 2023. Characteristic polynomials of random
    truncations: Moments, duality and asymptotics. Random Matrices: Theory and Applications.
    12(01), 2250049.'
  mla: 'Serebryakov, Alexander, et al. “Characteristic Polynomials of Random Truncations:
    Moments, Duality and Asymptotics.” <i>Random Matrices: Theory and Applications</i>,
    vol. 12, no. 01, 2250049, World Scientific Publishing, 2023, doi:<a href="https://doi.org/10.1142/s2010326322500496">10.1142/s2010326322500496</a>.'
  short: 'A. Serebryakov, N. Simm, G. Dubach, Random Matrices: Theory and Applications
    12 (2023).'
date_created: 2024-05-29T06:14:26Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2025-09-09T14:27:10Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/s2010326322500496
external_id:
  arxiv:
  - '2109.10331'
  isi:
  - '000848874400001'
intvolume: '        12'
isi: 1
issue: '01'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2109.10331
month: '01'
oa: 1
oa_version: Preprint
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Characteristic polynomials of random truncations: Moments, duality and asymptotics'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 12
year: '2023'
...
---
_id: '11135'
abstract:
- lang: eng
  text: We consider a correlated NxN Hermitian random matrix with a polynomially decaying
    metric correlation structure. By calculating the trace of the moments of the matrix
    and using the summable decay of the cumulants, we show that its operator norm
    is stochastically dominated by one.
article_number: '2250036'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jana
  full_name: Reker, Jana
  id: e796e4f9-dc8d-11ea-abe3-97e26a0323e9
  last_name: Reker
citation:
  ama: 'Reker J. On the operator norm of a Hermitian random matrix with correlated
    entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href="https://doi.org/10.1142/s2010326322500368">10.1142/s2010326322500368</a>'
  apa: 'Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated
    entries. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/s2010326322500368">https://doi.org/10.1142/s2010326322500368</a>'
  chicago: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
    Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing,
    2022. <a href="https://doi.org/10.1142/s2010326322500368">https://doi.org/10.1142/s2010326322500368</a>.'
  ieee: 'J. Reker, “On the operator norm of a Hermitian random matrix with correlated
    entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World
    Scientific Publishing, 2022.'
  ista: 'Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated
    entries. Random Matrices: Theory and Applications. 11(4), 2250036.'
  mla: 'Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated
    Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036,
    World Scientific Publishing, 2022, doi:<a href="https://doi.org/10.1142/s2010326322500368">10.1142/s2010326322500368</a>.'
  short: 'J. Reker, Random Matrices: Theory and Applications 11 (2022).'
corr_author: '1'
date_created: 2022-04-08T07:11:12Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2026-04-07T13:02:12Z
day: '01'
department:
- _id: GradSch
- _id: LaEr
doi: 10.1142/s2010326322500368
external_id:
  arxiv:
  - '2103.03906'
  isi:
  - '000848873800001'
intvolume: '        11'
isi: 1
issue: '4'
keyword:
- Discrete Mathematics and Combinatorics
- Statistics
- Probability and Uncertainty
- Statistics and Probability
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2103.03906'
month: '10'
oa: 1
oa_version: Preprint
publication: 'Random Matrices: Theory and Applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
related_material:
  record:
  - id: '17164'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: On the operator norm of a Hermitian random matrix with correlated entries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2022'
...
---
_id: '6488'
abstract:
- lang: eng
  text: We prove a central limit theorem for the difference of linear eigenvalue statistics
    of a sample covariance matrix W˜ and its minor W. We find that the fluctuation
    of this difference is much smaller than those of the individual linear statistics,
    as a consequence of the strong correlation between the eigenvalues of W˜ and W.
    Our result identifies the fluctuation of the spatial derivative of the approximate
    Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar
    result for Wigner matrices, for sample covariance matrices, the fluctuation may
    entirely vanish.
article_number: '2050006'
article_processing_charge: No
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
citation:
  ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics
    for sample covariance matrices. <i>Random Matrices: Theory and Application</i>.
    2020;9(3). doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a>'
  apa: 'Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear
    eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory
    and Application</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a>'
  chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of
    Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices:
    Theory and Application</i>. World Scientific Publishing, 2020. <a href="https://doi.org/10.1142/S2010326320500069">https://doi.org/10.1142/S2010326320500069</a>.'
  ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue
    statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>,
    vol. 9, no. 3. World Scientific Publishing, 2020.'
  ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue
    statistics for sample covariance matrices. Random Matrices: Theory and Application.
    9(3), 2050006.'
  mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear
    Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory
    and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020,
    doi:<a href="https://doi.org/10.1142/S2010326320500069">10.1142/S2010326320500069</a>.'
  short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).'
date_created: 2019-05-26T21:59:14Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2025-07-10T11:53:26Z
day: '01'
department:
- _id: LaEr
doi: 10.1142/S2010326320500069
ec_funded: 1
external_id:
  arxiv:
  - '1806.08751'
  isi:
  - '000547464400001'
intvolume: '         9'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1806.08751
month: '07'
oa: 1
oa_version: Preprint
project:
- _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: 'Random Matrices: Theory and Application'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Fluctuations for differences of linear eigenvalue statistics for sample covariance
  matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2020'
...
---
_id: '5971'
abstract:
- lang: eng
  text: "We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices
    H=H∗ with centered independent entries and with a general matrix of variances
    Sxy=\U0001D53C∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of
    the support of the self-consistent density of states. We establish a bound on
    this maximum in terms of norms of powers of S that substantially improves the
    earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality
    for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727].
    The key element of the proof is an effective Markov chain approximation for the
    contributions of the weighted Dyck paths appearing in the iterative solution of
    the corresponding Dyson equation."
article_number: '1950009'
article_processing_charge: No
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: Peter
  full_name: Mühlbacher, Peter
  last_name: Mühlbacher
citation:
  ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices.
    <i>Random matrices: Theory and applications</i>. 2018. doi:<a href="https://doi.org/10.1142/s2010326319500096">10.1142/s2010326319500096</a>'
  apa: 'Erdös, L., &#38; Mühlbacher, P. (2018). Bounds on the norm of Wigner-type
    random matrices. <i>Random Matrices: Theory and Applications</i>. World Scientific
    Publishing. <a href="https://doi.org/10.1142/s2010326319500096">https://doi.org/10.1142/s2010326319500096</a>'
  chicago: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type
    Random Matrices.” <i>Random Matrices: Theory and Applications</i>. World Scientific
    Publishing, 2018. <a href="https://doi.org/10.1142/s2010326319500096">https://doi.org/10.1142/s2010326319500096</a>.'
  ieee: 'L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,”
    <i>Random matrices: Theory and applications</i>. World Scientific Publishing,
    2018.'
  ista: 'Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices.
    Random matrices: Theory and applications., 1950009.'
  mla: 'Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random
    Matrices.” <i>Random Matrices: Theory and Applications</i>, 1950009, World Scientific
    Publishing, 2018, doi:<a href="https://doi.org/10.1142/s2010326319500096">10.1142/s2010326319500096</a>.'
  short: 'L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).'
date_created: 2019-02-13T10:40:54Z
date_published: 2018-09-26T00:00:00Z
date_updated: 2025-04-15T08:05:02Z
day: '26'
department:
- _id: LaEr
doi: 10.1142/s2010326319500096
ec_funded: 1
external_id:
  arxiv:
  - '1802.05175'
  isi:
  - '000477677200002'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1802.05175
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: 'Random matrices: Theory and applications'
publication_identifier:
  eissn:
  - 2010-3271
  issn:
  - 2010-3263
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bounds on the norm of Wigner-type random matrices
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2018'
...