Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions
Disordered Systems and Neural Networks
2015-06-23 v1 Mathematical Physics
math.MP
Abstract
We analyze the random Euclidean bipartite matching problem on the hypertorus in dimensions with quadratic cost and we derive the two--point correlation function for the optimal matching, using a proper ansatz introduced by Caracciolo et al. to evaluate the average optimal matching cost. We consider both the grid--Poisson matching problem and the Poisson--Poisson matching problem. We also show that the correlation function is strictly related to the Green's function of the Laplace operator on the hypertorus.
Keywords
Cite
@article{arxiv.1504.00614,
title = {Scaling hypothesis for the Euclidean bipartite matching problem II. Correlation functions},
author = {Sergio Caracciolo and Gabriele Sicuro},
journal= {arXiv preprint arXiv:1504.00614},
year = {2015}
}