Exact solution of the random bipartite matching model

TL;DR

This paper provides an exact solution for the average minimum energy in a random bipartite matching model with exponential interactions, confirming previous conjectures and replica results.

Contribution

It offers the first exact finite-size solution for the model, validating the Parisi conjecture and replica analysis in the thermodynamic limit.

Findings

Exact average minimum energy derived for finite systems

Confirms the Parisi conjecture for this model

Validates replica solution results in the thermodynamic limit

Abstract

In this paper we present the exact solution for the average minimum energy of the random bipartite matching model with an arbitrary finite number of elements where random paired interactions are described by independent exponential distribution. This solution confirms the Parisi conjecture proposed for this model earlier, as well as the result of the replica solution of this model in the thermodynamic limit.