Quenched invariance principle for simple random walk on discrete point processes
نویسندگان
چکیده
منابع مشابه
Quenched 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 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 Two-dimensional Percolation Clusters
We consider the simple random walk on a two-dimensional super-critical infinite percolation cluster. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to a non-degenerate Brownian motion.
متن کاملQuenched 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 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: Stochastic Processes and their Applications
سال: 2013
ISSN: 0304-4149
DOI: 10.1016/j.spa.2013.05.006