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 …

The asymptotic behavior of the integrated density of states for a randomly perturbed lattice at
the infimum of the spectrum is investigated. The leading term is determined when the decay …

We derive bounds on the integrated density of states for a class of Schrödinger operators
with a random potential. The potential depends on a sequence of random variables, not …

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 study low-energy properties of the random displacement model, a random Schrödinger
operator describing an electron in a randomly deformed lattice. All periodic displacement …

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 …