---
OA_place: repository
_id: '17352'
abstract:
- lang: eng
  text: "We prove upper bounds on the $L^\\infty$-Wasserstein distance from optimal\r\ntransport
    between strongly log-concave probability densities and log-Lipschitz\r\nperturbations.
    In the simplest setting, such a bound amounts to a\r\ntransport-information inequality
    involving the $L^\\infty$-Wasserstein metric\r\nand the relative $L^\\infty$-Fisher
    information. We show that this inequality\r\ncan be sharpened significantly in
    situations where the involved densities are\r\nanisotropic. Our proof is based
    on probabilistic techniques using Langevin\r\ndynamics. As an application of these
    results, we obtain sharp exponential rates\r\nof convergence in Fisher's infinitesimal
    model from quantitative genetics,\r\ngeneralising recent results by Calvez, Poyato,
    and Santambrogio in dimension 1\r\nto arbitrary dimensions."
article_number: '2402.04151'
article_processing_charge: No
arxiv: 1
author:
- first_name: Kseniia
  full_name: Khudiakova, Kseniia
  id: 4E6DC800-AE37-11E9-AC72-31CAE5697425
  last_name: Khudiakova
  orcid: 0000-0002-6246-1465
- first_name: Jan
  full_name: Maas, Jan
  id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
  last_name: Maas
  orcid: 0000-0002-0845-1338
- first_name: Francesco
  full_name: Pedrotti, Francesco
  id: d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
  last_name: Pedrotti
citation:
  ama: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave
    measures and exponential convergence in Fisher’s infinitesimal model. <i>arXiv</i>.
    doi:<a href="https://doi.org/10.48550/arXiv.2402.04151">10.48550/arXiv.2402.04151</a>
  apa: Khudiakova, K., Maas, J., &#38; Pedrotti, F. (n.d.). L∞-optimal transport of
    anisotropic log-concave measures and exponential convergence in Fisher’s infinitesimal
    model. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2402.04151">https://doi.org/10.48550/arXiv.2402.04151</a>
  chicago: Khudiakova, Kseniia, Jan Maas, and Francesco Pedrotti. “L∞-Optimal Transport
    of Anisotropic Log-Concave Measures and Exponential Convergence in Fisher’s Infinitesimal
    Model.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2402.04151">https://doi.org/10.48550/arXiv.2402.04151</a>.
  ieee: K. Khudiakova, J. Maas, and F. Pedrotti, “L∞-optimal transport of anisotropic
    log-concave measures and exponential convergence in Fisher’s infinitesimal model,”
    <i>arXiv</i>. .
  ista: Khudiakova K, Maas J, Pedrotti F. L∞-optimal transport of anisotropic log-concave
    measures and exponential convergence in Fisher’s infinitesimal model. arXiv, 2402.04151.
  mla: Khudiakova, Kseniia, et al. “L∞-Optimal Transport of Anisotropic Log-Concave
    Measures and Exponential Convergence in Fisher’s Infinitesimal Model.” <i>ArXiv</i>,
    2402.04151, doi:<a href="https://doi.org/10.48550/arXiv.2402.04151">10.48550/arXiv.2402.04151</a>.
  short: K. Khudiakova, J. Maas, F. Pedrotti, ArXiv (n.d.).
corr_author: '1'
date_created: 2024-07-31T08:07:40Z
date_published: 2024-02-07T00:00:00Z
date_updated: 2026-04-07T13:00:02Z
day: '07'
department:
- _id: JaMa
doi: 10.48550/arXiv.2402.04151
external_id:
  arxiv:
  - '2402.04151'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2402.04151
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
  grant_number: F6504
  name: Taming Complexity in Partial Differential Systems
- _id: 34d33d68-11ca-11ed-8bc3-ec13763c0ca8
  grant_number: '26293'
  name: The impact of deleterious mutations on small populations
publication: arXiv
publication_status: draft
related_material:
  record:
  - id: '20050'
    relation: later_version
    status: public
  - id: '17336'
    relation: dissertation_contains
    status: public
status: public
title: L∞-optimal transport of anisotropic log-concave measures and exponential convergence
  in Fisher's infinitesimal model
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...