Related papers: Almost sure functional central limit theorem for b…
Consider the dynamic environment governed by a Poissonian field of independent particles evolving as simple random walks on $\mathbb{Z}^d$. The random walk on random walks model refers to a particular stochastic process on $\mathbb{Z}^d$…
We prove a quenched functional central limit theorem (quenched FCLT) for the sums of a random field (r.f.) along a Z d-random walk in different frameworks: probabilistic (when the r.f. is i.i.d. or a moving average of i.i.d. random…
We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability…
We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently by Rassoul-Agha and Sepp\"al\"ainen in [10] and Berger and Zeitouni in…
We obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks on the simplex of probability measures over a finite set. Due to a reinforcement mechanism, the increments of the walks are…
Consider the invariance principle for a random walk with random environment (denoted by $\mu$) in time on $\bfR$ in a weak quenched sense. We show that a sequence of the random probability measures on $\bfR$ generated by a bounded Lipschitz…
We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…
We consider random walks in a balanced random environment in $\mathbb{Z}^d$, $d\geq 2$. We first prove an invariance principle (for $d\ge2$) and the transience of the random walks when $d\ge 3$ (recurrence when $d=2$) in an ergodic…
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 a functional CLT for the quenched expected position of the…
We derive a functional central limit theorem for the excursion of a random walk conditioned on sweeping a prescribed geometric area. We assume that the increments of the random walk are integer-valued, centered, with a third moment equal to…
A short proof of the quenched central limit theorem for the random walk in random environment introduced by Boldrighini, Minlos, and Pellegrinotti is given.
We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…
We consider a model for random walks on random environments (RWRE) with random subset of Z^d as the vertices, and uniform transition probabilities on 2d points (two "coordinate nearest points" in each of the d coordinate directions). We…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
We study the asymptotic behaviour of random walks in i.i.d. non-elliptic random environments on $\mathbb{Z}^d$. Standard conditions (and proofs) for ballisticity and the central limit theorem require ellipticity. We use oriented percolation…
We consider random walks in dynamic random environments, with an environment generated by the time-reversal of a Markov process from the oriented percolation universality class. If the influence of the random medium on the walk is small in…
In this paper, we establish an almost sure central limit theorem for a general random sequence under a strong approximation condition. Additionally, we derive the law of the iterated logarithm for the center of mass corresponding to a…
A transient stochastic process is considered strongly transient if conditioned on returning to the starting location, the expected time it takes to return the the starting location is finite. We characterize strong transience for a…
This thesis concerns the study of random walks in random environments (RWRE). Since there are two levels of randomness for random walks in random environments, there are two different distributions for the random walk that can be studied.…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…