English

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 d>1d>1, 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}
}