## Electronic Communications in Probability

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

Justin Salez

#### 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).

#### Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 13, 7 pp.

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

https://projecteuclid.org/euclid.ecp/1465320940

Digital Object Identifier
doi:10.1214/ECP.v20-3791

Mathematical Reviews number (MathSciNet)
MR3314648

Zentralblatt MATH identifier
1353.60011

Rights

#### Citation

Salez, Justin. The Mézard-Parisi equation for matchings in pseudo-dimension $d&gt;1$. Electron. Commun. Probab. 20 (2015), paper no. 13, 7 pp. doi:10.1214/ECP.v20-3791. https://projecteuclid.org/euclid.ecp/1465320940

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