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