We prove spectral and dynamical localization for the multidimensional random displacement
model near the bottom of its spectrum by showing that the approach through multiscale …

The survival problem for a diffusing particle moving among random traps is considered. We
introduce a simple argument to derive the quenched asymptotics of the survival probability …

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 …

We consider the annealed asymptotics for the survival probability of Brownian motion
among randomly distributed traps. The configuration of the traps is given by independent …

We study the Integrated Density of States (IDS) of the random Schr\" odinger operator
appearing in the study of certain reinforced random processes in connection with a …

The parabolic Anderson problem with a random potential obtained by attaching a long tailed
potential around a randomly perturbed lattice is studied. The moment asymptotics of the total …

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 …

For the Schrödinger operators on L2 (R2) and L2 (R3) with the uniform magnetic field and
the scalar potentials located at all sites of a randomly perturbed lattice, the asymptotic …

The Donsker-Varadhan theory on large deviations [12] and the Malliavin calculus [43] are
the main theories in the stochastic analysis founded in the latter twentieth century. Among …

For the Schrödinger operators on L2 (R2) and L2 (R3) with the uniform magnetic field and
the scalar potentials located at all sites of a randomly perturbed lattice, the asymptotic …