A correlation inequality for the symmetric exclusion process
Let \((\eta_ t)_{t\geq 0}\) denote the symmetric exclusion process on \(X=\{0,1\}^ S\) where S is finite or countable. The author shows that for any disjoint subsets A, B of S \[ (*)\quad P(\prod_{x\in A\cup B}\eta_ t(x)=1)\leq P(\prod_{x\in A}\eta_ t(x)=1)P(\prod_{x\in B}\eta_ t(x)=1),\quad t\geq 0. \] This extends a well-known correlation inequality [cf. \textit{T. M. Liggett}, ``Interacting particle systems'' (1985; Zbl 0559.60078)]. Restricting himself to the case in which \(S=Z^ d\) and the transition matrix is symmetric, translation invariant and irreducible, the author derives a pointwise ergodic theorem using (*).
scientific article; zbMATH DE number 4046869