---
_id: '13145'
abstract:
- lang: eng
  text: We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary
    finite diffuse measure space. We provide an interpretation of this characterization
    in analogy with the Mecke identity for Poisson point processes.
acknowledgement: Research supported by the Sfb 1060 The Mathematics of Emergent Effects
  (University of Bonn). L.D.S. gratefully acknowledges funding of his current position
  by the Austrian Science Fund (FWF) through project ESPRIT 208.
article_processing_charge: No
article_type: original
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
- first_name: Eugene
  full_name: Lytvynov, Eugene
  last_name: Lytvynov
citation:
  ama: Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson
    measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a
    href="https://doi.org/10.1214/23-ECP528">10.1214/23-ECP528</a>
  apa: Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization
    of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>.
    Institute of Mathematical Statistics. <a href="https://doi.org/10.1214/23-ECP528">https://doi.org/10.1214/23-ECP528</a>
  chicago: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
    of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>.
    Institute of Mathematical Statistics, 2023. <a href="https://doi.org/10.1214/23-ECP528">https://doi.org/10.1214/23-ECP528</a>.
  ieee: L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson
    measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute
    of Mathematical Statistics, pp. 1–12, 2023.
  ista: Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson
    measure. Electronic Communications in Probability. 28, 1–12.
  mla: Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization
    of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>,
    vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href="https://doi.org/10.1214/23-ECP528">10.1214/23-ECP528</a>.
  short: L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28
    (2023) 1–12.
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2023-12-13T11:24:57Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
external_id:
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oa_version: Published Version
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- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
  grant_number: E208
  name: Configuration Spaces over Non-Smooth Spaces
publication: Electronic Communications in Probability
publication_identifier:
  eissn:
  - 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Mecke-type characterization of the Dirichlet–Ferguson measure
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type: journal_article
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volume: 28
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...
---
_id: '12683'
abstract:
- lang: eng
  text: We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗
    for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In
    particular, we establish that with high probability, an outlier can be distinguished
    at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines
    elements of Hermitian and non-Hermitian analysis, and illustrates some aspects
    of the intrinsic instability of (even weakly) non-Hermitian matrices.
acknowledgement: G. Dubach gratefully acknowledges funding from the European Union’s
  Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond”
  No. 101020331.
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: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
citation:
  ama: Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix.
    <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href="https://doi.org/10.1214/23-ECP516">10.1214/23-ECP516</a>
  apa: Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of
    a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute
    of Mathematical Statistics. <a href="https://doi.org/10.1214/23-ECP516">https://doi.org/10.1214/23-ECP516</a>
  chicago: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation
    of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute
    of Mathematical Statistics, 2023. <a href="https://doi.org/10.1214/23-ECP516">https://doi.org/10.1214/23-ECP516</a>.
  ieee: G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian
    matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of
    Mathematical Statistics, pp. 1–13, 2023.
  ista: Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian
    matrix. Electronic Communications in Probability. 28, 1–13.
  mla: Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of
    a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28,
    Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href="https://doi.org/10.1214/23-ECP516">10.1214/23-ECP516</a>.
  short: G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.
date_created: 2023-02-26T23:01:01Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2023-10-17T12:48:10Z
day: '08'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/23-ECP516
ec_funded: 1
external_id:
  arxiv:
  - '2108.13694'
  isi:
  - '000950650200005'
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  date_created: 2023-02-27T09:43:27Z
  date_updated: 2023-02-27T09:43:27Z
  file_id: '12692'
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  file_size: 479105
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has_accepted_license: '1'
intvolume: '        28'
isi: 1
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 1-13
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '754411'
  name: ISTplus - Postdoctoral Fellowships
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
publication: Electronic Communications in Probability
publication_identifier:
  eissn:
  - 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamics of a rank-one perturbation of a Hermitian matrix
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type: journal_article
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...