Conditions for ballisticity and invariance principle for random walk in non-elliptic random environment
نویسندگان
چکیده
منابع مشابه
Quenched Invariance Principle for Multidimensional Ballistic Random Walk in a Random Environment with a Forbidden Direction
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. We prove an invariance principle (functional central limit theorem) under almost every fixed environment. The assumptions are nonnestling, at least two spatial dimensions, and a 2 + ε moment for the step of the walk uniformly in the environment. The main point behind ...
متن کاملQuenched invariance principle for random walks in balanced random environment
We consider random walks in a balanced random environment in Z , d ≥ 2. We first prove an invariance principle (for d ≥ 2) and the transience of the random walks when d ≥ 3 (recurrence when d = 2) in an ergodic environment which is not uniformly elliptic but satisfies certain moment condition. Then, using percolation arguments, we show that under mere ellipticity, the above results hold for ran...
متن کاملQuenched Exit Estimates and Ballisticity Conditions for Higher-dimensional Random Walk in Random Environment by Alexander Drewitz
Consider a random walk in an i.i.d. uniformly elliptic environment in dimensions larger than one. In 2002 Sznitman introduced for each γ ∈ (0, 1) the ballisticity condition (T )γ and the condition (T ′) defined as the fulfillment of (T )γ for each γ ∈ (0, 1). Sznitman proved that (T ′) implies a ballistic law of large numbers. Furthermore, he showed that for all γ ∈ (0.5, 1), (T )γ is equivalen...
متن کاملQuenched Invariance Principle for Simple Random Walk on Percolation Clusters
We consider the simple random walk on the (unique) infinite cluster of super-critical percolation in Z with d ≥ 2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate Brownian motion.
متن کاملQuenched invariance principle for simple random walk on percolation clusters
We consider the simple random walk on the (unique) infinite cluster of supercritical bond percolation in Z with d ≥ 2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2017
ISSN: 1083-6489
DOI: 10.1214/17-ejp107