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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...
A self-similar process arising from a random walk with random environment in random scenery
birth–death process random environment random scenery random walk self-similar process
2011/3/24
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion ...
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...
Random Walk in Dynamic Markovian Random Environment
Random Walk Markovian Random Environment
2009/6/12
Random Walk in Dynamic Markovian Random Environment.
Ballistic random walk in a random environment with a forbidden direction
ballistic random walk random environment forbidden direction
2009/6/12
Ballistic random walk in a random environment with a forbidden.
A Non-Ballistic Law of Large Numbers for Random Walks in I.I.D. Random Environment
random walk in random environment RWRE law of large numbers
2009/4/29
We prove that random walks in i.i.d. random environments which oscillate in a given direction have velocity zero with respect to that direction. This complements existing results thus giving a general...
Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
random walk in a random environment mixingmeasure
2009/4/29
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
A Condition for Weak Disorder for Directed Polymers in Random Environment
Directed polymer in random environment weak disorder size-biasing
2009/4/28
We give a sufficient criterion for the weak disorder regime of directed polymers in random environment, which extends a well-known second moment criterion. We use a stochastic representation of the si...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Random walk random environment zero-one law law of large numbers
2009/4/24
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...
Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
random walk random environment
2009/4/22
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
On the Zero-One Law and the Law of Large Numbers for Random Walk in Mixing Random Environment
Zero-One Law Random Walk Mixing Random Environment
2009/4/7
We prove a weak version of the law of large numbers for multi-dimensional finite range random walks in certain mixing elliptic random environments. This already improves previously existing results, w...