The Mezard-Parisi equation for matchings in pseudo-dimension d>1
Probability
2014-09-10 v1
Abstract
We establish existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension , as conjectured by Aldous and Bandyopadhyay (Annals of Applied Probability, 2005) and W\"astlund (Annals of Mathematics, 2012). This fills the last remaining gap in the proof of the original M\'ezard-Parisi prediction for this problem (Journal de Physique Lettres, 1985).
Keywords
Cite
@article{arxiv.1409.2813,
title = {The Mezard-Parisi equation for matchings in pseudo-dimension d>1},
author = {Justin Salez},
journal= {arXiv preprint arXiv:1409.2813},
year = {2014}
}