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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...
Random walk in deterministically changing environment
Random Walk Random environment Dynamical Systems CLT Transfer operator
2009/6/12
We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic,but strongly chaotic,evolution.We prove that for almost all initial conditions of the en...
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...
Invariance principles for standard-normalized and self-normalized random fields
Functional central limit theorem invariance principle i.i.d. random elds martingale-dierence random elds Orlicz spaces metric entropy self-normalization
2009/6/12
We investigate the invariance principle for set-indexed partial sums of a stationary field (X ) d of martingale-di?erence or independent random variables kk-Z under standard normalization or self-norm...