Random Jumps in Evolving Random Environment

#### C. Boldrighini, Yu.G. Kondratiev, R.A. Minlos, A. Pellegrinotti, E. Zhizhina

2008, v.14, Issue 4, 543-570

ABSTRACT

We consider a particle moving in $R^d$ according to a jump Markov process and interacting with an evolving random environment. The latter is represented by a stationary Glauber type dynamics in the continuum. Assuming a low activity - high temperature regime for the Glauber dynamics and small coupling between particle and environment, we obtain the large time asymptotics for the particle position distribution.

Keywords: jump Markov processes,birth-and-death process,continuous system,Gibbs measure,Glauber dynamics,random environment