We discuss the long time behaviour of the parabolic Anderson model, the Cauchy problem
for the heat equation with random potential on Z^ d. We consider general iid potentials and …

This is a continuation of our previous work [6] on the investigation of intermittency for the
parabolic equation (∂/∂ t) u= H u on ℝ+× ℤ d associated with the Anderson Hamiltonian …

This paper is devoted to the analysis of the large time behavior of the solutions of the
Anderson parabolic problem: ∂ u ∂ t= κ Δ u ξ (x) u when the potential ξ (x) is a …

This is a survey on the intermittent behavior of the parabolic Anderson model, which is the
Cauchy problem for the heat equation with random potential on the lattice ℤ d. We first …

The objective of this paper is a mathematically rigorous investigation of intermittency and
related questions intensively studied in different areas of physics, in particular in …

We consider the parabolic Anderson problem∂ tu= Δ u+ ξ (x) u on ℝ+× ℤ d with localized
initial condition u (0, x)= δ 0 (x) and random iid potential ξ. Under the assumption that the …

The parabolic Anderson problem is the Cauchy problem for the heat equation with random
potential and localized initial condition. In this paper, we consider potentials which are …

Consider the Cauchy problem∂ u (x, t)/∂ t= ℋ u (x, t)(x∈ ℤ d, t≥ 0) with initial condition u
(x, 0)≡ 1 and with ℋ the Anderson Hamiltonian ℋ= κΔ+ ξ. Here Δ is the discrete Laplacian …

The parabolic Anderson model is the Cauchy problem for the heat equation with a random
potential. We consider this model in a setting which is continuous in time and discrete in …

This is a comprehensive survey on the research on the parabolic Anderson model–the heat
equation with random potential or the random walk in random potential–of the years 1990 …