Fluctuations in the random-link matching problem
arXiv:1905.08529 · doi:10.1103/PhysRevE.100.032102
Abstract
Using the replica approach and the cavity method, we study the fluctuations of the optimal cost in the random-link matching problem. By means of replica arguments, we derive the exact expression of its variance. Moreover, we study the large deviation function, deriving its expression in two different ways, namely using both the replica method and the cavity method.
9 pages, 3 figures