Sharp PDE estimates for random two-dimensional bipartite matching with power cost function
Analysis of PDEs
2024-05-16 v1 Combinatorics
Probability
Abstract
We investigate the random bipartite optimal matching problem on a flat torus in two-dimensions, considering general strictly convex power costs of the distance. We extend the successful ansatz first introduced by Caracciolo et al. for the quadratic case, involving a linear Poisson equation, to a non-linear equation of -Poisson type, allowing for a more comprehensive analysis of the optimal transport cost. Our results establish new asymptotic connections between the energy of the solution to the PDE and the optimal transport cost, providing insights on their asymptotic behavior.
Cite
@article{arxiv.2405.09397,
title = {Sharp PDE estimates for random two-dimensional bipartite matching with power cost function},
author = {Luigi Ambrosio and Federico Vitillaro and Dario Trevisan},
journal= {arXiv preprint arXiv:2405.09397},
year = {2024}
}