We introduce a statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail… (More)

The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a time-dependent… (More)

We continue our study of intermittency for the parabolic Anderson model ∂u/∂t = κ∆u + ξu in a space-time random medium ξ, where κ is a positive di usion constant, ∆ is the lattice Laplacian on Zd, d… (More)

Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by… (More)

We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η : Z × [0,∞) → {0, 1} with simple random walk transition kernel, starting from a… (More)

In this paper we study the parabolic Anderson equation ∂u(x, t)/∂t = κ∆u(x, t) + ξ(x, t)u(x, t), x ∈ Z, t ≥ 0, where the u-field and the ξ-field are R-valued, κ ∈ [0,∞) is the diffusion constant, and… (More)

We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η : Z 2 × [0, ∞) → {0, 1} with simple random walk transition kernel, starting from a… (More)

We consider the parabolic Anderson model ∂u/∂ t = κ∆u + γξ u with u : Zd×R+→R+, where κ ∈R+ is the diffusion constant, ∆ is the discrete Laplacian, γ ∈ R+ is the coupling constant, and ξ :… (More)

We consider some questions raised by the recent paper of Gantert, Löwe and Steif (2005) concerning " signed " voter models on locally finite graphs. These are voter model like processes with the… (More)

We consider some questions raised by the recent paper of Gantert, Löwe and Steif (2005) concerning " signed " voter models on locally finite graphs. These are voter model like processes with the… (More)