Cluster expansion for locally interacting Markov chains (Q1117604)

The authors discuss the continuity properties of small perturbations of Markov chains with the phase space \(U^{{\mathbb{Z}}^{\nu}}\), where U is a countable set. It is proved that if the transition probabilities for the Markov chain can be represented as \(p_ 0+\delta c\) and \(p_ 0\) possesses a good Lyapunov function, then the perturbed Markov chain also converges to a stationary state provided that the initial probability distribution satisfies certain conditions. The limiting state depends analytically on \(\delta\) in some circle \(\{\delta \in {\mathbb{C}}:| \delta | <\delta_ 0\}\).