Electronic Communications in Probability

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

Justin Salez

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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

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

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

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Zentralblatt MATH identifier

Primary: 60C05: Combinatorial probability
Secondary: 82B44: Disordered systems (random Ising models, random Schrödinger operators, etc.) 90C35: Programming involving graphs or networks [See also 90C27]

Recursive distributional equation Random assignment problem Cavity method

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Salez, Justin. The Mézard-Parisi equation for matchings in pseudo-dimension $d>1$. 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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