Current Distribution and random matrix ensembles for an integrable asymmetric fragmentation process

TL;DR

This paper analyzes a discrete-time fragmentation process, deriving exact solutions and showing that the current distribution aligns with the largest eigenvalue distribution of Gaussian unitary ensembles, highlighting universality in the KPZ class.

Contribution

It provides an exact determinant solution for the process and links the current distribution to random matrix theory, revealing universality in the KPZ class.

Findings

Current distribution matches the GUE largest eigenvalue distribution

The process's scaling limit confirms KPZ universality

Establishes a link between integrable systems and random matrices

Abstract

We calculate the time-evolution of a discrete-time fragmentation process in which clusters of particles break up and reassemble and move stochastically with size-dependent rates. In the continuous-time limit the process turns into the totally asymmetric simple exclusion process (only pieces of size 1 break off a given cluster). We express the exact solution of master equation for the process in terms of a determinant which can be derived using the Bethe ansatz. From this determinant we compute the distribution of the current across an arbitrary bond which after appropriate scaling is given by the distribution of the largest eigenvalue of the Gaussian unitary ensemble of random matrices. This result confirms universality of the scaling form of the current distribution in the KPZ universality class and suggests that there is a link between integrable particle systems and random matrix ensembles.