Random Jumps in Evolving Random Environment
2008, v.14, №4, 543-570
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