---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
PlanS_conform: '1'
_id: '20591'
abstract:
- lang: eng
  text: In this paper we derive estimates for the Hessian of the logarithm (log-Hessian)
    for solutions to the heat equation. For initial data in the form of log-Lipschitz
    perturbation of strongly log-concave measures, the log-Hessian admits an explicit,
    uniform (in space) lower bound. This yields a new estimate for the Lipschitz constant
    of a transport map pushing forward the standard Gaussian to a measure in this
    class. On the other hand, we show that assuming only fast decay of the tails of
    the initial datum does not suffice to guarantee uniform log-Hessian upper bounds.
acknowledgement: This research was funded in part by the Austrian Science Fund (FWF)
  project 10.55776/F65 and by the European Union’s Horizon 2020 research and innovation
  programme under the Marie Sklodowska-Curie grant agreement No 101034413. The authors
  thank Professors Jean Dolbeault, Jan Maas, and Nikita Simonov for many useful comments,
  and Professors Kazuhiro Ishige, Asuka Takatsu, and Yair Shenfeld for inspiring interactions.
article_number: '71'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Giovanni
  full_name: Brigati, Giovanni
  id: 63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  last_name: Brigati
- first_name: Francesco
  full_name: Pedrotti, Francesco
  id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
  last_name: Pedrotti
citation:
  ama: Brigati G, Pedrotti F. Heat flow, log-concavity, and Lipschitz transport maps.
    <i>Electronic Communications in Probability</i>. 2025;30. doi:<a href="https://doi.org/10.1214/25-ECP717">10.1214/25-ECP717</a>
  apa: Brigati, G., &#38; Pedrotti, F. (2025). Heat flow, log-concavity, and Lipschitz
    transport maps. <i>Electronic Communications in Probability</i>. Institute of
    Mathematical Statistics. <a href="https://doi.org/10.1214/25-ECP717">https://doi.org/10.1214/25-ECP717</a>
  chicago: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and
    Lipschitz Transport Maps.” <i>Electronic Communications in Probability</i>. Institute
    of Mathematical Statistics, 2025. <a href="https://doi.org/10.1214/25-ECP717">https://doi.org/10.1214/25-ECP717</a>.
  ieee: G. Brigati and F. Pedrotti, “Heat flow, log-concavity, and Lipschitz transport
    maps,” <i>Electronic Communications in Probability</i>, vol. 30. Institute of
    Mathematical Statistics, 2025.
  ista: Brigati G, Pedrotti F. 2025. Heat flow, log-concavity, and Lipschitz transport
    maps. Electronic Communications in Probability. 30, 71.
  mla: Brigati, Giovanni, and Francesco Pedrotti. “Heat Flow, Log-Concavity, and Lipschitz
    Transport Maps.” <i>Electronic Communications in Probability</i>, vol. 30, 71,
    Institute of Mathematical Statistics, 2025, doi:<a href="https://doi.org/10.1214/25-ECP717">10.1214/25-ECP717</a>.
  short: G. Brigati, F. Pedrotti, Electronic Communications in Probability 30 (2025).
corr_author: '1'
date_created: 2025-11-02T23:01:35Z
date_published: 2025-09-25T00:00:00Z
date_updated: 2025-12-01T15:08:54Z
day: '25'
ddc:
- '500'
department:
- _id: JaMa
doi: 10.1214/25-ECP717
ec_funded: 1
external_id:
  arxiv:
  - '2404.15205'
  isi:
  - '001611557000018'
file:
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fulldoi: https://doi.org/10.1214/25-ECP717
has_accepted_license: '1'
intvolume: '        30'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Electronic Communications in Probability
publication_identifier:
  eissn:
  - 1083-589X
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
title: Heat flow, log-concavity, and Lipschitz transport maps
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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2025'
...
---
DOAJ_listed: '1'
OA_place: repository
OA_type: gold
_id: '18655'
abstract:
- lang: eng
  text: "Let Qd be the d-dimensional binary hypercube. We say that P={v1,…,vk} is
    an increasing path of length k−1 in Qd, if for every i∈[k−1] the edge vivi+1 is
    obtained by switching some zero coordinate in vi to a one coordinate in vi+1.\r\nForm
    a random subgraph Qdp by retaining each edge in E(Qd) independently with probability
    p. We show that there is a phase transition with respect to the length of a longest
    increasing path around p=ed. Let α be a constant and let p=αd. When α<e, then
    there exists a δ∈[0,1) such that whp a longest increasing path in Qdp is of length
    at most δd. On the other hand, when α>e, whp there is a path of length d−2 in
    Qdp, and in fact, whether it is of length d−2,d−1, or d depends on whether the
    all-zero and all-one vertices percolate or not."
acknowledgement: "Research supported by the European Union’s Horizon 2020 research
  and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101034413.\r\nThe
  authors wish to thank Ross Pinsky for his comments on an earlier version of the
  paper, and for bringing reference [12] to our attention. The authors are grateful
  to the anonymous referees for their helpful comments and suggestions."
article_number: '70'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Michael
  full_name: Anastos, Michael
  id: 0b2a4358-bb35-11ec-b7b9-e3279b593dbb
  last_name: Anastos
- first_name: Sahar
  full_name: Diskin, Sahar
  last_name: Diskin
- first_name: Dor
  full_name: Elboim, Dor
  last_name: Elboim
- first_name: Michael
  full_name: Krivelevich, Michael
  last_name: Krivelevich
citation:
  ama: Anastos M, Diskin S, Elboim D, Krivelevich M. Climbing up a random subgraph
    of the hypercube. <i>Electronic Communications in Probability</i>. 2024;29. doi:<a
    href="https://doi.org/10.1214/24-ECP639">10.1214/24-ECP639</a>
  apa: Anastos, M., Diskin, S., Elboim, D., &#38; Krivelevich, M. (2024). Climbing
    up a random subgraph of the hypercube. <i>Electronic Communications in Probability</i>.
    Duke University Press. <a href="https://doi.org/10.1214/24-ECP639">https://doi.org/10.1214/24-ECP639</a>
  chicago: Anastos, Michael, Sahar Diskin, Dor Elboim, and Michael Krivelevich. “Climbing
    up a Random Subgraph of the Hypercube.” <i>Electronic Communications in Probability</i>.
    Duke University Press, 2024. <a href="https://doi.org/10.1214/24-ECP639">https://doi.org/10.1214/24-ECP639</a>.
  ieee: M. Anastos, S. Diskin, D. Elboim, and M. Krivelevich, “Climbing up a random
    subgraph of the hypercube,” <i>Electronic Communications in Probability</i>, vol.
    29. Duke University Press, 2024.
  ista: Anastos M, Diskin S, Elboim D, Krivelevich M. 2024. Climbing up a random subgraph
    of the hypercube. Electronic Communications in Probability. 29, 70.
  mla: Anastos, Michael, et al. “Climbing up a Random Subgraph of the Hypercube.”
    <i>Electronic Communications in Probability</i>, vol. 29, 70, Duke University
    Press, 2024, doi:<a href="https://doi.org/10.1214/24-ECP639">10.1214/24-ECP639</a>.
  short: M. Anastos, S. Diskin, D. Elboim, M. Krivelevich, Electronic Communications
    in Probability 29 (2024).
corr_author: '1'
date_created: 2024-12-15T23:01:51Z
date_published: 2024-11-24T00:00:00Z
date_updated: 2025-09-09T11:46:53Z
day: '24'
ddc:
- '510'
department:
- _id: MaKw
doi: 10.1214/24-ECP639
ec_funded: 1
external_id:
  arxiv:
  - '2311.16631'
  isi:
  - '001356019700001'
file:
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  checksum: 307a9d049325e6ca9bfe8b4a1f275983
  content_type: application/pdf
  creator: dernst
  date_created: 2024-12-16T07:33:34Z
  date_updated: 2024-12-16T07:33:34Z
  file_id: '18657'
  file_name: 2024_ElectrCommProbability_Anastos.pdf
  file_size: 530169
  relation: main_file
  success: 1
file_date_updated: 2024-12-16T07:33:34Z
fulldoi: https://doi.org/10.1214/24-ECP639
has_accepted_license: '1'
intvolume: '        29'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2311.16631
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Electronic Communications in Probability
publication_identifier:
  eissn:
  - 1083-589X
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Climbing up a random subgraph of the hypercube
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 29
year: '2024'
...
---
_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.
corr_author: '1'
date_created: 2023-02-26T23:01:01Z
date_published: 2023-02-08T00:00:00Z
date_updated: 2025-04-14T07:44:00Z
day: '08'
ddc:
- '510'
department:
- _id: LaEr
doi: 10.1214/23-ECP516
ec_funded: 1
external_id:
  arxiv:
  - '2108.13694'
  isi:
  - '000950650200005'
file:
- access_level: open_access
  checksum: a1c6f0a3e33688fd71309c86a9aad86e
  content_type: application/pdf
  creator: dernst
  date_created: 2023-02-27T09:43:27Z
  date_updated: 2023-02-27T09:43:27Z
  file_id: '12692'
  file_name: 2023_ElectCommProbability_Dubach.pdf
  file_size: 479105
  relation: main_file
  success: 1
file_date_updated: 2023-02-27T09:43:27Z
fulldoi: https://doi.org/10.1214/23-ECP516
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
tmp:
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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2023'
...
---
_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.
corr_author: '1'
date_created: 2023-06-18T22:00:48Z
date_published: 2023-05-05T00:00:00Z
date_updated: 2025-04-14T12:59:08Z
day: '05'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1214/23-ECP528
external_id:
  isi:
  - '001042025400001'
file:
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  checksum: 4a543fe4b3f9e747cc52167c17bfb524
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  creator: dernst
  date_created: 2023-06-19T09:37:40Z
  date_updated: 2023-06-19T09:37:40Z
  file_id: '13152'
  file_name: 2023_ElectronCommProbability_Schiavo.pdf
  file_size: 271434
  relation: main_file
  success: 1
file_date_updated: 2023-06-19T09:37:40Z
fulldoi: https://doi.org/10.1214/23-ECP528
has_accepted_license: '1'
intvolume: '        28'
isi: 1
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1-12
project:
- _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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  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2023'
...