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Sharp PDE estimates for random two-dimensional bipartite matching with power cost function by Ambrosio, Luigi; Vitillaro, Federico; Trevisan, Dario is a scholarly article available to read on EtoBox.

What is Sharp PDE estimates for random two-dimensional bipartite matching with power cost function about?

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 $q$-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.

Author

Ambrosio, Luigi; Vitillaro, Federico; Trevisan, Dario

Published

2024

Language

EN