A PDE approach to a 2-dimensional matching problem View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-02

AUTHORS

Luigi Ambrosio, Federico Stra, Dario Trevisan

ABSTRACT

We prove asymptotic results for 2-dimensional random matching problems. In particular, we obtain the leading term in the asymptotic expansion of the expected quadratic transportation cost for empirical measures of two samples of independent uniform random variables in the square. Our technique is based on a rigorous formulation of the challenging PDE ansatz by Caracciolo et al. (Phys Rev E 90:012118, 2014) that linearizes the Monge–Ampère equation. More... »

PAGES

433-477

References to SciGraph publications

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  • 1995-01. Asymptotics for transportation cost in high dimensions in JOURNAL OF THEORETICAL PROBABILITY
  • 1987. Etude des transformations de Riesz dans les variétés riemanniennes à courbure de Ricci minorée in SÉMINAIRE DE PROBABILITÉS XXI
  • 2000-01. A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem in NUMERISCHE MATHEMATIK
  • 2011. Introduction to Measure Theory and Integration in NONE
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    URI

    http://scigraph.springernature.com/pub.10.1007/s00440-018-0837-x

    DOI

    http://dx.doi.org/10.1007/s00440-018-0837-x

    DIMENSIONS

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