Related papers: One-dimensional random interlacements
We consider the two-dimensional simple random walk conditioned on never hitting the origin. This process is a Markov chain, namely it is the Doob $h$-transform of the simple random walk with respect to the potential kernel. It is known to…
We prove CLTs for biased randomly trapped random walks in one dimension. In particular, we will establish an annealed invariance principal by considering a sequence of regeneration times under the assumption that the trapping times have…
We consider simple random walk on a discrete cylinder with base a large d-dimensional torus of side-length N, when d is two or more. We develop a stochastic domination control on the local picture left by the random walk in boxes of…
Consider a continuous time random walk in $\mathbb{Z}$ with independent and exponentially distributed jumps $\pm1$. The model in this paper consists in an infinite number of such random walks starting from the complement of…
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…
We study the random walk in random environment on {0,1,2,...}, where the environment is subject to a vanishing (random) perturbation. The two particular cases we consider are: (i) random walk in random environment perturbed from Sinai's…
We consider a random walk in an i.i.d. non-negative potential on the d-dimensional integer lattice. The walk starts at the origin and is conditioned to hit a remote location y on the lattice. We prove that the expected time under the…
We consider transient nearest-neighbor random walks in random environment on Z. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level n, around…
We consider transient random walks on a strip in a random environment. The model was introduced by Bolthausen and Goldsheid [Comm. Math. Phys. 214 (2000) 429--447]. We derive a strong law of large numbers for the random walks in a general…
Let a simple random walk run inside a torus of dimension three or higher for a number of steps which is a constant proportion of the volume. We examine geometric properties of the range, the random subgraph induced by the set of vertices…
We consider random interlacements on Z^d, with d bigger or equal to 3, when their vacant set is in a strongly percolative regime. We derive an asymptotic upper bound on the probability that the random interlacements disconnect a box of…
We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
A Random Walk in Changing Environment (RWCE) is a weighted random walk on a locally finite, connected graph $G$ with random, time-dependent edge-weights. This includes self-interacting random walks, where the edge-weights depend on the…
There is a long history of establishing central limit theorems for Markov chains. Quantitative bounds for chains with a spectral gap were proved by Mann and refined later. Recently, rates of convergence for the total variation distance were…
We consider a transient random walk on $Z^d$ which is asymptotically stable, without centering, in a sense which allows different norming for each component. The paper is devoted to the asymptotics of the probability of the first return to…
Consider a one dimensional simple random walk $X=(X_n)_{n\geq0}$. We form a new simple symmetric random walk $Y=(Y_n)_{n\geq0}$ by taking sums of products of the increments of $X$ and study the two-dimensional walk…
We investigate random walks on complex networks and derive an exact expression for the mean first passage time (MFPT) between two nodes. We introduce for each node the random walk centrality $C$, which is the ratio between its coordination…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…