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

Justin Salez 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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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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