Large deviations for random walks in random environment on a Galton-Watson tree

Consider a random walk in random environment on a supercritical Galton–Watson tree, and let n be the hitting time of generation n. The paper presents a large deviation principle for n/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.