The Mézard-Parisi equation for matchings in pseudo-dimension \(d > 1\)
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 \textit{D. J. Aldous} and \textit{A. Bandyopadhyay} [Ann. Appl. Probab. 15, No. 2, 1047--1110 (2005; Zbl 1105.60012)] and \textit{J. Wästlund} [Ann. Math. (2) 175, No. 3, 1061--1091 (2012; Zbl 1262.91046)].
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