@article{fcc006663a8c4330ba36c7c68bac497c,
title = "Random Assignment Problems on 2d Manifolds",
abstract = "We consider the assignment problem between two sets of N random points on a smooth, two-dimensional manifold Ω of unit area. It is known that the average cost scales as EΩ(N) ∼ 1 / 2 πln N with a correction that is at most of order lnNlnlnN. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first Ω -dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace–Beltrami operator on Ω. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics.",
keywords = "assignment, disorder, finite-size corrections, matching, optimal transportation, random optimization problems",
author = "D. Benedetto and E. Caglioti and S. Caracciolo and M. D{\textquoteright}Achille and G. Sicuro and A. Sportiello",
note = "Funding Information: E. Caglioti and G. Sicuro would like to thank Giorgio Parisi for putting them in contact. D. Benedetto and E. Caglioti thanks Gabriele Mondello and Riccardo Salvati Manni for clarifying discussions about the case of the torus. The authors are grateful to J{\"u}rg Fr{\"o}hlich for his careful reading of the manuscript. A. Sportiello is partially supported by the Agence Nationale de la Recherche, Grant Number ANR-18-CE40-0033 (ANR DIMERS). Funding Information: E.?Caglioti and G.?Sicuro would like to thank Giorgio Parisi for putting them in contact. D.?Benedetto and E.?Caglioti thanks Gabriele Mondello and Riccardo Salvati Manni for clarifying discussions about the case of the torus. The authors are grateful to J?rg Fr?hlich for his careful reading of the manuscript. A.?Sportiello is partially supported by the Agence Nationale de la Recherche, Grant Number ANR-18-CE40-0033 (ANR DIMERS). Publisher Copyright: {\textcopyright} 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = may,
doi = "10.1007/s10955-021-02768-4",
language = "English",
volume = "183",
pages = "1--40",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "2",
}