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

1 Modélisation stochastique
LPMA - Laboratoire de Probabilités et Modèles Aléatoires
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).
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Cited literature [16 references]

https://hal.archives-ouvertes.fr/hal-01062106
Contributor : Justin Salez <>
Submitted on : Tuesday, September 9, 2014 - 11:16:22 AM
Last modification on : Friday, March 27, 2020 - 3:47:34 AM
Document(s) archivé(s) le : Wednesday, December 10, 2014 - 11:30:44 AM

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### Citation

Justin Salez. The Mezard-Parisi equation for matchings in pseudo-dimension d>1. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2015, 20, ⟨10.1214/ECP.v20-3791⟩. ⟨hal-01062106⟩

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