an:05223441
Zbl 1141.82015
Chayes, Lincoln; Liggett, Thomas M.
One dimensional nearest neighbor exclusion processes in inhomogeneous and random environ\-ments
EN
J. Stat. Phys. 129, No. 2, 193-203 (2007).
0022-4715 1572-9613
2007
j
82C70 82C22
exclusion processes; nonreversible stationary distributions
The authors discuss the existence problem of reversible and nonreversible stationary distributions for the exclusion processes in inhomogeneous and random environments. They prove that for an exclusion process with i.i.d. \(p_i\)'s,, if there is a \(\varepsilon>0\) such that \(P(p_0\geq \frac{1}{2}-\varepsilon)>0\) and \(P(p_0\leq \frac{1}{2}+\varepsilon)>0\), then all stationary distributions are reversible; if for some \(\varepsilon>0\) such that \(P(p_0<\frac{1}{2}-\varepsilon)=1\) or \(P(p_0>\frac{1}{2}=\varepsilon)=1\), then there exists a nonreversible stationary distribution. In the cases of an i.i.d. environment, they got a necessary and sufficient condition for the existence of nonreversible stationary distributions.
Gen Qi Xu (Tianjin)