Related papers: Invariance Principle and recurrence for random wal…

This paper has been withdrawn by the author due to the incorrect argument for the security.

A zero-one law of Engelbert--Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin's lemma play key roles.

The paper has been withdrawn by the author, due to a critical error stemming from the defined template.

This paper is withdrawn from submission due to a critical error in the proof of main theorem.

This paper has been withdrawn by the author due to a gap in the proof of the main result.

This paper has been withdrawn by the author because there are some typos in proofs.

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if…

This paper has been withdrawn by the author.

The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.

In this paper, we consider random walk in random environment on $\mathbb{Z}^{d}\,(d\geq1)$ and prove the Strassen's strong invariance principle for this model, via martingale argument and the theory of fractional coboundaries of Derriennic…

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance…

We prove an invariance principle for the bridge of a random walk conditioned to stay positive, when the random walk is in the domain of attraction of a stable law, both in the discrete and in the absolutely continuous setting. This includes…

This paper has been withdrawn by the authors, due to a crucial error in beta functions.

This paper has been withdrawn by the author because the result of this paper was already obtained.

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…

Title: An unlikely result Authors: T.M. Other Comments: This paper has been withdrawn Abstract: This paper has been withdrawn by the author due to the fact that some of the results turned out to be known.

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…

This paper has been withdrawn by the author due to an error.

This paper has been withdrawn by the authors due to need of essential revision.