摘要：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).
关键词：Recursive distributional equation; Random assignment problem; Cavity method;60C05; 82B44; 90C35
