# Fluctuations in the random-link matching problem

## TL;DR

This paper analyzes the fluctuations of the optimal cost in the random-link matching problem using advanced statistical physics methods, deriving exact variance and large deviation functions.

## Contribution

It provides the first exact expressions for the variance and large deviation functions in the random-link matching problem.

## Key findings

- Exact variance of optimal cost derived
- Large deviation function characterized
- Methods applicable to related combinatorial problems

## 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.