A PDE approach to a 2-dimensional matching problem

By Luigi Ambrosio, Federico Stra, Dario Trevisan. 2016

147 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fa7bff8ab43b6f7aea9e6b5393d4d40cb583ddb1

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In Applied Mathematics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Central limit theorems for empirical transportation cost in general dimension (2017, methodology): “In a different setting using PDE, rates in dimension 2 are also given [2].”