---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Giovanni
      foaf_name: Brigati, Giovanni
      foaf_surname: Brigati
      foaf_workInfoHomepage: http://www.librecat.org/personId=63ff57e8-1fbb-11ee-88f2-f558ffc59cf1
  - foaf_Person:
      foaf_givenName: Francesco
      foaf_name: Pedrotti, Francesco
      foaf_surname: Pedrotti
      foaf_workInfoHomepage: http://www.librecat.org/personId=d3ac8ac6-dc8d-11ea-abe3-e2a9628c4c3c
  bibo_doi: 10.1214/25-ECP717
  bibo_volume: 30
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001611557000018
  dct_isPartOf:
  - http://id.crossref.org/issn/1083-589X
  dct_language: eng
  dct_publisher: Institute of Mathematical Statistics@
  dct_title: Heat flow, log-concavity, and Lipschitz transport maps@
...