Document Zbl 1353.60011

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The Mézard-Parisi equation for matchings in pseudo-dimension \(d > 1\). (English) Zbl 1353.60011

Electron. Commun. Probab. 20, Paper No. 13, 7 p. (2015).

This paper establishes existence and uniqueness of the solution to the cavity equation for the random assignment problem in pseudo-dimension \(d>1\), as conjectured by D. J. Aldous and A. Bandyopadhyay [Ann. Appl. Probab. 15, No. 2, 1047–1110 (2005; Zbl 1105.60012)] and J. Wästlund [Ann. Math. (2) 175, No. 3, 1061–1091 (2012; Zbl 1262.91046)].

Reviewer: Ping Sun (Shenyang)

MSC:

60C05	Combinatorial probability
82B44	Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics
90C35	Programming involving graphs or networks

Keywords:

recursive distributional equation; random assignment problem; cavity method

Citations:

Zbl 1105.60012; Zbl 1262.91046

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