Related papers: Invariance principles for random walks in cones

We develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that…

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…

In this paper, we establish the invariance principle and the large deviation for the biased random walk $RW_{\lambda}$ with $\lambda \in [0,1)$ on $\mathbb{Z}^d, d\geq 1$.

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over…

Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk…

We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…

We consider simple random walks on random graphs embedded in $\mathbb{R}^d$ and generated by point processes such as Delaunay triangulations, Gabriel graphs and the creek-crossing graphs. Under suitable assumptions on the point process, we…

We consider simple random walks on Delaunay triangulations generated by point processes in $\mathbb{R}^d$. Under suitable assumptions on the point processes, we show that the random walk satisfies an almost sure (or quenched) invariance…

We study a continuous time random walk $X$ in an environment of i.i.d. random conductances $\mu_e\in[1,\infty)$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when…

The primary purpose of this article is to prove a tightness of skew random walks. The tightness result implies, in particular, that the skew Brownian motion can be constructed as the scaling limit of such random walks. Our proof of…

We construct a renewal structure for random walks on surface groups. The renewal times are defined as times when the random walks enters a particular type of a cone and never leaves it again. As a consequence, the trajectory of the random…

We consider a random walk among a Poisson cloud of moving traps on ${\mathbb Z}^d$, where the walk is killed at a rate proportional to the number of traps occupying the same position. In dimension $d=1$, we have previously shown that under…

In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying spaces converge with respect to the…

We study a continuous time random walk, $X$, on ${\mathbb{Z}}^d$ in an environment of random conductances taking values in $(0,\infty)$. We assume that the law of the conductances is ergodic with respect to space shifts. We prove a quenched…

We consider a random walk $\{S_n\}_{n\in \mathbb{N}}$ in time-inhomogeneous random environment $\xi$. For almost each realization of $\xi$, we formulate a quenched harmonic function, based on which we can define the random walk in random…

We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.

We give three different criteria for transience of a Branching Markov Chain. These conditions enable us to give a classification of Branching Random Walks in Random Environment (BRWRE) on Cayley Graphs in recurrence and transience. This…

Some asymptotic properties of a Brownian motion in multifractal time, also called multifractal random walk, are established. We show the almost sure and $L^1$ convergence of its structure function. This is an issue directly connected to the…

Recent progress in the understanding of quenched invariance principles (QIP) for a continuous-time random walk on $\mathbb{Z}^d$ in an environment of dynamical random conductances is reviewed and extended to the $1$-dimensional case. The…

We prove the almost sure ('quenched') invariance principle for a random walker on an infinite Bernoulli percolation cluster in $\Z^d$ where $d$ is larger or equal than 2.