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The Voter Model in a Random Environment in Z^d
voter model random walk random environment duality
2016/1/25
We consider the voter model with flip rates determined by(μ e ,e ∈ E d ), where E d is the set of all non-oriented nearest-neighbour edges in the Euclidean lattice Z d . Suppose that (μ e ,e ∈ E d ) a...
Shape and local growth for multidimensional branching random walks in random environment
Shape theorem subadditive ergodic theorem transience growth ex-ponent population size
2009/6/12
We study branching random walks in random environment on the d-dimensional square lattice, d 1. In this model, the environment has nite range dependence, and the population size cannot decrease. We pr...
Strong disorder implies strong localization for directed polymers in a random environment
Directed polymers Random environment strong disorder localization parabolic Anderson
2009/6/12
In this note we show that in any dimension d, the strong disorder property implies the strong localization property. This is established for a continuous time model of directed polymersin arandom envi...