This monograph contains the notes of lectures I gave in Saint Flour Probability Summer
School in July 2016. The two other courses were given by Paul Bourgade and by Scott …

Although time-dependent random media with short-range correlations lead to (possibly
biased) normal tracer diffusion, anomalous fluctuations occur away from the most probable …

In 2003, Varadhan (Comm. Pure Appl. Math. 56 (2003) 1222–1245) developed a robust
method for proving quenched and averaged large deviations for random walks in a …

We consider the quenched and the averaged (or annealed) large deviation rate functions I q
and I a for space-time and (the usual) space-only RWRE on Z^ d. By Jensen's inequality, I …

We consider random walks in random Dirichlet environment (RWDE) which is a special type
of random walks in random environment where the exit probabilities at each site are iid …

In this work, we establish the existence of large deviation principles of random walk in
strongly mixing environments. The quenched and annealed rate functions have the same …

We consider random walk in a uniformly elliptic iid random environment in ℤd for d≥ 2. It is
believed that whenever the random walk is transient in a given direction it is necessarily …

In this paper we introduce and study renewal–reward processes in random environments
where each renewal involves a reward taking values in a Banach space. We derive …

For a random walk in a uniformly elliptic and iid environment on Z d with d≥ 4, we show that
the quenched and annealed large deviation rate functions agree on any compact set …

In this paper we introduce and study renewal-reward processes in random environments
where each renewal involves a reward taking values in a Banach space. We derive …