We consider the stirring process in the interval $\Lambda_N:=[-N,N]$ of $\mathbb Z$ with births and deaths taking place in the intervals $I_+:=(N-K,N]$, and respectively $I_-:=[-N,-N+K)$, $1 \le K <N$. We prove bounds on the truncated moments uniform in $N$ which yield strong factorization properties.
"Truncated correlations in the stirring process with births and deaths." Electron. J. Probab. 17 1 - 35, 2012. https://doi.org/10.1214/EJP.v17-1734