We study homogenization properties of the discrete Laplace operator with random
conductances on a large domain in Z^d. More precisely, we prove almost-sure …

We prove an invariance principle for the two-dimensional lattice parabolic Anderson model
with small potential. As applications we deduce a Donsker type convergence result for a …

The aim of this paper is to study asymptotic geometric properties almost surely or/and in
probability of extreme order statistics of an iid random field (potential) indexed by sites of …

We study paths of time-length t of a continuous-time random walk on ℤ² subject to self-
interaction that depends on the geometry of the walk range and a collection of random …

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 …

Let ξ ξ be a Gaussian white noise on R^ d R d (d= 1, 2, 3 d= 1, 2, 3). Let (ξ _ ε) _ ε> 0 (ξ ε) ε>
0 be continuous Gaussian processes such that ξ _ ε → ξ ξ ε→ ξ as ε → 0 ε→ 0, defined by …

This work is devoted to the asymptotic behavior of eigenvalues of an elliptic operator with
rapidly oscillating random coefficients on a bounded domain with Dirichlet boundary …

We consider random Schrödinger operators with Dirichlet boundary conditions outside
lattice approximations of a smooth Euclidean domain and study the behavior of its lowest …

Charge and exciton transport in disordered media plays an essential role in modern
technologies. Classical examples are amorphous and organic semiconductors where the …

In this chapter, we discuss much stronger and more detailed assertions about intermittency
than we did before. They characterise the long-time behaviour of the mass flow through a …