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2015 The Mézard-Parisi equation for matchings in pseudo-dimension $d>1$
Justin Salez
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Electron. Commun. Probab. 20: 1-7 (2015). DOI: 10.1214/ECP.v20-3791


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 Mézard-Parisi equation for matchings in pseudo-dimension $d>1$." Electron. Commun. Probab. 20 1 - 7, 2015.


Accepted: 14 February 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1353.60011
MathSciNet: MR3314648
Digital Object Identifier: 10.1214/ECP.v20-3791

Primary: 60C05
Secondary: 82B44 , 90C35

Keywords: Cavity method , random assignment problem , recursive distributional equation

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