Ballistic Random Walk in a Random Environment with a Forbidden Direction
نویسندگان
چکیده
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance principle. The assumptions are non-nestling and 1 + ε (resp. 2 + ε) moments for the step of the walk uniformly in the environment, for the law of large numbers (resp. invariance principles). We also investigate invariance principles under fixed environments, and invariance principles for the environment-dependent mean of the walk.
منابع مشابه
Quenched Invariance Principle for Multidimensional Ballistic Random Walk in a Random Environment with a Forbidden Direction by Firas Rassoul-agha
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 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 کاملAlmost sure functional central limit theorem for ballistic random walk in random environment
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched me...
متن کاملFluctuations of the quenched mean of a planar random walk in an i.i.d. random environment with forbidden direction
We consider an i.i.d. random environment with a strong form of transience on the two dimensional integer lattice. Namely, the walk always moves forward in the y-direction. We prove an invariance principle for the quenched expected position of the random walk indexed by its level crossing times. We begin with a variation of the Martingale Central Limit Theorem. The main part of the paper checks ...
متن کاملOn a general many-dimensional excited random walk
The generalized excited random walk is a generalization of the excited random walk, introduced in 2003 by Benjamini and Wilson, which is a discrete-time stochastic process (Xn, n = 0, 1, 2, . . .) taking values on Z, d ≥ 2, described as follows: when the particle visits a site for the first time, it has a uniformly positive drift in a given direction l; when the particle is at a site which was ...
متن کامل