Replica symmetry of the minimum matching

Abstract

We establish the soundness of the replica symmetric ansatz introduced by M. Mézard and G. Parisi for the minimum matching problem in the pseudo-dimension $d$ mean field model for $d\geq 1$. The case $d=1$ corresponds to the $\pi^2/6$-limit for the assignment problem proved by D. Aldous in 2001.
We introduce a game-theoretical framework by which we establish the analogous limit also for $d>1$.