Resumen de Large deviations for random walk in random environment with holding times

Amir Dembo, Nina Gantert, Ofer Zeitouni

• Suppose that the integers are assigned the random variables {ωx,μx} (taking values in the unit interval times the space of probability measures on \reals+), which serve as an environment. This environment defines a random walk {Xt} (called a RWREH) which, when at x, waits a random time distributed according to μx and then, after one unit of time, moves one step to the right with probability ωx, and one step to the left with probability 1−ωx. We prove large deviation principles for Xt/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.