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

2014/09/09 by Justin Salez, Salez, Justin · 1 citation
Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR

paper · pdf · doi:10.48550/arxiv.1409.2813

arxiv created 2014/09/09 · openalex publication_date 2014/09/09 · arxiv updated 2014/09/10 · openalex created_date 2022/08/17 · openalex updated_date 2026/07/28

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 Wästlund (Annals of Mathematics, 2012). This fills the last remaining gap in the proof of the original Mézard-Parisi prediction for this problem (Journal de Physique Lettres, 1985).

Cited by

• Uniqueness and locality of the ground state of the disordered Monomer-Dimer models on independently weighted Unimodular Bienaymé-Galton-Watson trees

Related

• Replica Symmetry and Combinatorial Optimization
• The Minimum Perfect Matching in Pseudo-dimension 0
• Mean field matching and TSP in pseudo-dimension 1
• A Proof of Parisi's Conjecture on the Random Assignment Problem
• A proof of a conjecture of Buck, Chan and Robbins on the random assignment problem