---
_id: '14667'
abstract:
- lang: eng
  text: 'For large dimensional non-Hermitian random matrices X with real or complex
    independent, identically distributed, centered entries, we consider the fluctuations
    of f (X) as a matrix where f is an analytic function around the spectrum of X.
    We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits
    Gaussian fluctuations as the matrix size grows to infinity, which consists of
    two independent modes corresponding to the tracial and traceless parts of A. We
    find a new formula for the variance of the traceless part that involves the Frobenius
    norm of A and the L2-norm of f on the boundary of the limiting spectrum. '
- lang: fre
  text: On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne
    de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction
    analytique sur un domaine qui contient le spectre de X. On prouve que, pour une
    matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A
    sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant
    aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie
    pour la variance de la composante de trace nulle, qui fait intervenir la norme
    de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.
acknowledgement: "The first author was partially supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated
  editor for carefully reading this paper and providing helpful comments that improved
  the quality of the article. Also the authors would like to thank Peter Forrester
  for pointing out the reference [12] that was absent in the previous version of the
  manuscript."
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: Hong Chang
  full_name: Ji, Hong Chang
  id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
  last_name: Ji
citation:
  ama: Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. <i>Annales
    de l’institut Henri Poincare (B) Probability and Statistics</i>. 2023;59(4):2083-2105.
    doi:<a href="https://doi.org/10.1214/22-AIHP1304">10.1214/22-AIHP1304</a>
  apa: Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random
    matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/22-AIHP1304">https://doi.org/10.1214/22-AIHP1304</a>
  chicago: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
    Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>.
    Institute of Mathematical Statistics, 2023. <a href="https://doi.org/10.1214/22-AIHP1304">https://doi.org/10.1214/22-AIHP1304</a>.
  ieee: L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,”
    <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol.
    59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.
  ista: Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales
    de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105.
  mla: Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random
    Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>,
    vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:<a
    href="https://doi.org/10.1214/22-AIHP1304">10.1214/22-AIHP1304</a>.
  short: L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and
    Statistics 59 (2023) 2083–2105.
date_created: 2023-12-10T23:01:00Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2023-12-11T12:36:56Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-AIHP1304
ec_funded: 1
external_id:
  arxiv:
  - '2112.11382'
intvolume: '        59'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2112.11382
month: '11'
oa: 1
oa_version: Preprint
page: 2083-2105
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Annales de l'institut Henri Poincare (B) Probability and Statistics
publication_identifier:
  issn:
  - 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Functional CLT for non-Hermitian random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2023'
...
---
_id: '14750'
abstract:
- lang: eng
  text: "Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N ×
    N deterministic matrices and U is either an N × N Haar unitary or orthogonal random
    matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991)
    201–220), the limiting empirical spectral distribution (ESD) of the above model
    is given by the free multiplicative convolution\r\nof the limiting ESDs of A and
    B, denoted as μα \x02 μβ, where μα and μβ are the limiting ESDs of A and B, respectively.
    In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues
    and eigenvectors statistics. We prove that both the density of μA \x02μB, where
    μA and μB are the ESDs of A and B, respectively and the associated subordination
    functions\r\nhave a regular behavior near the edges. Moreover, we establish the
    local laws near the edges on the optimal scale. In particular, we prove that the
    entries of the resolvent are close to some functionals depending only on the eigenvalues
    of A, B and the subordination functions with optimal convergence rates. Our proofs
    and calculations are based on the techniques developed for the additive model
    A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017)
    947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and
    our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020)
    108639) for the multiplicative model. "
acknowledgement: "The first author is partially supported by NSF Grant DMS-2113489
  and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported
  by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to
  thank the Editor, Associate Editor and an anonymous referee for their many critical
  suggestions which have significantly improved the paper. We also want to thank Zhigang
  Bao and Ji Oon Lee for many helpful discussions and comments."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Xiucai
  full_name: Ding, Xiucai
  last_name: Ding
- first_name: Hong Chang
  full_name: Ji, Hong Chang
  id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
  last_name: Ji
citation:
  ama: Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals
    of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href="https://doi.org/10.1214/22-aap1882">10.1214/22-aap1882</a>
  apa: Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices.
    <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics.
    <a href="https://doi.org/10.1214/22-aap1882">https://doi.org/10.1214/22-aap1882</a>
  chicago: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random
    Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical
    Statistics, 2023. <a href="https://doi.org/10.1214/22-aap1882">https://doi.org/10.1214/22-aap1882</a>.
  ieee: X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,”
    <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical
    Statistics, pp. 2981–3009, 2023.
  ista: Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The
    Annals of Applied Probability. 33(4), 2981–3009.
  mla: Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.”
    <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical
    Statistics, 2023, pp. 2981–3009, doi:<a href="https://doi.org/10.1214/22-aap1882">10.1214/22-aap1882</a>.
  short: X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.
date_created: 2024-01-08T13:03:18Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2024-01-09T08:16:41Z
day: '01'
department:
- _id: LaEr
doi: 10.1214/22-aap1882
ec_funded: 1
external_id:
  arxiv:
  - '2010.16083'
intvolume: '        33'
issue: '4'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2010.16083
month: '08'
oa: 1
oa_version: Preprint
page: 2981-3009
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: The Annals of Applied Probability
publication_identifier:
  issn:
  - 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local laws for multiplication of random matrices
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2023'
...
---
_id: '14780'
abstract:
- lang: eng
  text: In this paper, we study the eigenvalues and eigenvectors of the spiked invariant
    multiplicative models when the randomness is from Haar matrices. We establish
    the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩
    for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence
    rates. Moreover, we prove that the non-outlier eigenvalues stick with those of
    the unspiked matrices and the non-outlier eigenvectors are delocalized. The results
    also hold near the so-called BBP transition and for degenerate spikes. On one
    hand, our results can be regarded as a refinement of the counterparts of [12]
    under additional regularity conditions. On the other hand, they can be viewed
    as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar
    random matrix.
acknowledgement: The authors would like to thank the editor, the associated editor
  and two anonymous referees for their many critical suggestions which have significantly
  improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee
  for many helpful discussions. The first author also wants to thank Hari Bercovici
  for many useful comments. The first author is partially supported by National Science
  Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant
  “RMTBeyond” No. 101020331.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Xiucai
  full_name: Ding, Xiucai
  last_name: Ding
- first_name: Hong Chang
  full_name: Ji, Hong Chang
  id: dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d
  last_name: Ji
citation:
  ama: Ding X, Ji HC. Spiked multiplicative random matrices and principal components.
    <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href="https://doi.org/10.1016/j.spa.2023.05.009">10.1016/j.spa.2023.05.009</a>
  apa: Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and
    principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier.
    <a href="https://doi.org/10.1016/j.spa.2023.05.009">https://doi.org/10.1016/j.spa.2023.05.009</a>
  chicago: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices
    and Principal Components.” <i>Stochastic Processes and Their Applications</i>.
    Elsevier, 2023. <a href="https://doi.org/10.1016/j.spa.2023.05.009">https://doi.org/10.1016/j.spa.2023.05.009</a>.
  ieee: X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal
    components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier,
    pp. 25–60, 2023.
  ista: Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components.
    Stochastic Processes and their Applications. 163, 25–60.
  mla: Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and
    Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol.
    163, Elsevier, 2023, pp. 25–60, doi:<a href="https://doi.org/10.1016/j.spa.2023.05.009">10.1016/j.spa.2023.05.009</a>.
  short: X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023)
    25–60.
date_created: 2024-01-10T09:29:25Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2024-01-16T08:49:51Z
day: '01'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1016/j.spa.2023.05.009
ec_funded: 1
external_id:
  arxiv:
  - '2302.13502'
  isi:
  - '001113615900001'
file:
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  date_created: 2024-01-16T08:47:31Z
  date_updated: 2024-01-16T08:47:31Z
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  file_size: 1870349
  relation: main_file
  success: 1
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has_accepted_license: '1'
intvolume: '       163'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 25-60
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Stochastic Processes and their Applications
publication_identifier:
  eissn:
  - 1879-209X
  issn:
  - 0304-4149
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Spiked multiplicative random matrices and principal components
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  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: 163
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...