Large deviations for random walk in random environment with holding times

Ofer Zeitouni, Nina Gantert, Amir Dembo
2004 Annals of Probability  
Suppose that the integers are assigned the random variables {ω x , µ x } (taking values in the unit interval times the space of probability measures on R + ), which serve as an environment. This environment defines a random walk {X t } (called a RWREH) which, when at x, waits a random time distributed according to µ x and then, after one unit of time, moves one step to the right with probability ω x , and one step to the left with probability 1 − ω x . We prove large deviation principles for X
more » ... /t, both quenched (i.e., conditional upon the environment), with deterministic rate function, and annealed (i.e., averaged over the environment). As an application, we show that for random walks on Galton-Watson trees, quenched and annealed rate functions along a ray differ.
doi:10.1214/aop/1079021470 fatcat:djfeku4cynbatnexwegxqzgigq