Replica symmetry of the minimum matching
Journal article, 2012
We establish the soundness of the replica symmetric ansatz introduced by M. Mezard and G. Parisi for the minimum matching problem in the pseudo-dimension d mean field model for d >= 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.
zeta(2) limit
parisi
mean-field
equations
asymptotics
proof
weak-convergence
local
traveling-salesman problem
random assignment problem
spin-glasses
Author
Johan Wästlund
Chalmers, Mathematical Sciences, Mathematics
University of Gothenburg
Annals of Mathematics
0003-486X (ISSN)
Vol. 175 3 1061-1091Subject Categories (SSIF 2011)
Mathematics
DOI
10.4007/annals.2012.175.3.2