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 …

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 …

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 …

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 …

We consider the parabolic Anderson problem∂ tu= κΔ u+ ξ (x) u on R+× Rd with initial
condition u (0, x)= 1. Here ξ (·) is a random shift-invariant potential having high δ-like peaks …

We consider the parabolic Anderson model∂∂ tvn= κ Δ nv n+ ξ nvn on the n-dimensional
hypercube {− 1,+ 1} n with random iid potential ξ n. We study vn at the location of the k th …

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 study limit behavior for sums of the form 1| L| x ∈ L u (t, x), where the
field\Lambda_L=\left {x ∈ Z^ d:| x| ≤ L\right\} is composed of solutions of the parabolic …

(Aƒ)(z)= Σ [ƒ (y)− f (z)], for ze Zd, ƒ: Zd→ R yezd ly-z= 1 is the discrete Laplacian, and the
potential (§ (z): z€ Zd) is a collection of independent identically distributed random variables …