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arXiv · 1409.2813

The Mezard-Parisi equation for matchings in pseudo-dimension d>1

Justin Salez
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Abstract

We establish existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension $d>1$, 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).

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Justin Salez. 2014-09-09. The Mezard-Parisi equation for matchings in pseudo-dimension d>1. https://arxiv.org/abs/1409.2813

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