We study the stochastic heat equation (SHE)∂ tu= 1 2 Δ u+ β u ξ driven by a multiplicative
Lévy noise ξ with positive jumps and coupling constant β> 0, in arbitrary dimension d≥ 1 …

We consider random walks on the nonnegative integers in a space-time dependent random
environment. We assume that transition probabilities are given by independent Beta (μ, μ) …

The effect of disorder for pinning models is a subject which has attracted much attention in
theoretical physics and rigorous mathematical physics. A peculiar point of interest is the …

Random walk in a dynamic iid beta random environment, conditioned to escape at an
atypical velocity, converges to a Doob transform of the original walk. The Doob-transformed …

We give two variational formulas (qVar1) and (qVar2) for the quenched free energy of a
random walk in random potential (RWRP) when (i) the underlying walk is directed or …

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

Abstract We consider the Random Walk Pinning Model studied in Birkner-Sun 2008 and
Birkner-Greven-den Hollander 2008: this is a random walk X on Z^d, whose law is modified …

We investigate the high-temperature behavior of the directed polymer model in dimension
1+2. More precisely we study the difference ΔF(β) between the quenched and annealed free …

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 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 …