Exponential convergence for attractive reversible subcritical nearest particle systems
The exponential convergence to zero of the probability that a site is occupied is proved for a nearest particle system on integers. The flip rates are defined, for a configuration \(\gamma\) at site \(x\), by \(c(x, \gamma) = 1\) if \(\gamma (x) = 1\) and \(c(x, \gamma) = \beta (l_x, r_x) \geq 0\) if \(\gamma (x) = 0\), where \(l_x\) and \(r_x\) are the distances to the first occupied site at the left, or at the right side to \(x\), respectively. A special form of \(\beta\) is investigated and the system is supposed to be reversible, attractive, Feller, and subcritical (the only invariant measure is \(\gamma = 0\) with probability one). Some uniform bound on the values \(\beta (l,r)\) is needed.
scientific article; zbMATH DE number 828752