---
res:
  bibo_abstract:
  - We study a random matching problem on closed compact  2 -dimensional Riemannian
    manifolds (with respect to the squared Riemannian distance), with samples of random
    points whose common law is absolutely continuous with respect to the volume measure
    with strictly positive and bounded density. We show that given two sequences of
    numbers  n  and  m=m(n)  of points, asymptotically equivalent as  n  goes to infinity,
    the optimal transport plan between the two empirical measures  μn  and  νm  is
    quantitatively well-approximated by  (Id,exp(∇hn))#μn  where  hn  solves a linear
    elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère
    equation. This is obtained in the case of samples of correlated random points
    for which a stretched exponential decay of the  α -mixing coefficient holds and
    for a class of discrete-time Markov chains having a unique absolutely continuous
    invariant measure with respect to the volume measure.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Nicolas
      foaf_name: Clozeau, Nicolas
      foaf_surname: Clozeau
      foaf_workInfoHomepage: http://www.librecat.org/personId=fea1b376-906f-11eb-847d-b2c0cf46455b
  - foaf_Person:
      foaf_givenName: Francesco
      foaf_name: Mattesini, Francesco
      foaf_surname: Mattesini
  bibo_doi: 10.1007/s00440-023-01254-0
  bibo_volume: 190
  dct_date: 2024^xs_gYear
  dct_identifier:
  - UT:001136206200002
  dct_isPartOf:
  - http://id.crossref.org/issn/0178-8051
  - http://id.crossref.org/issn/1432-2064
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: Annealed quantitative estimates for the quadratic 2D-discrete random
    matching problem@
...