Truncated correlations in the stirring process with births and deaths

TL;DR

This paper studies a stirring process with births and deaths in a finite interval, establishing bounds on moments and demonstrating strong factorization properties that enhance understanding of the process's correlations.

Contribution

It introduces bounds on truncated moments for the stirring process with births and deaths, revealing new factorization properties uniform in system size.

Findings

Bounds on truncated moments are uniform in N.

Strong factorization properties are established.

Enhanced understanding of correlations in the process.

Abstract

We consider the stirring process in the interval $\La_N:=[-N,N]$ of $\mathbb Z$ with births and deaths taking place in the intervals $I_+:=(N-K,N]$, $K>0$, and respectively $I_-:=[-N,-N+K)$. We prove bounds on the truncated moments uniform in $N$ which yield strong factorization properties.