There have been extensive studies of a random walk among a field of immobile traps (or
obstacles), where one is interested in the probability of survival as well as the law of the …

Place an obstacle with probability 1-p 1-p independently at each vertex of Z^ d Z d, and run
a simple random walk before hitting one of the obstacles. For d ≥ 2 d≥ 2 and p strictly …

Place an obstacle with probability 1-p independently at each vertex of Z^d, and run a simple
random walk until hitting one of the obstacles. For d\geq2 and p strictly above the critical …

We consider the Feynman-Kac functional associated with a Brownian motion in a random
potential. The potential is defined by attaching a heavy tailed positive potential around the …

This is a continuation of our earlier work [Stochastic Processes and their Applications, 129
(1), pp. 102–128, 2019] on the random walk in random scenery and in random layered …

We consider a one-dimensional simple random walk killed by quenched soft obstacles. The
position of the obstacles is drawn according to a renewal process with a power-law …

This is a survey of the parabolic Anderson model (PAM), the Cauchy problem for the heat
equation with random potential. This model and many variants and related models are …

We study the quenched long time behaviour of the survival probability up to time t, E xe−∫ 0
t V ω (X s) ds, E_x\lefte^-∫_0^tV^ω(X_s)ds\right, of a symmetric Lévy process with jumps …

V ω (Zs) ds)] associated with a pure-jump symmetric Lévy process (Zt) t⩾ 0 in general
Poissonian random potentials V ω on Rd, which is closely related to the large time …

A quenched large deviation principle for Brownian motion in a stationary potential is proved.
As the proofs are based on a method developed by Sznitman [Comm. Pure Appl. Math. 47 …