Related papers: Snakes and perturbed random walks

We prove that a law of large numbers and a central limit theorem hold for the excited random walk model in every dimension $d \geq 2$.

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between…

Consider the extreme value of a Bernoulli random walk on the one-dimensional integer lattice, with reflection at 0, over a finite discrete time interval. Only the asymmetric (biased) case is discussed. Asymptotic mean/variance results are…

We consider one-dimensional excited random walks with finitely many cookies at each site. There are certain natural monotonicity results that are known for the excited random walk under some partial orderings of the cookie environments. We…

Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…

Let $\{S_n\}$ be a random walk in the domain of attraction of a stable law $\mathcal{Y}$, i.e. there exists a sequence of positive real numbers $(a_n)$ such that $S_n/a_n$ converges in law to $\mathcal{Y}$. Our main result is that the…

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…

We study a non-reversible random walk advected by the symmetric simple exclusion process, so that the walk has a local drift of opposite sign when sitting atop an occupied or an empty site. We prove that the back-tracking probability of the…

We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided…

A random walk with echoed steps (RWES) is a process $\{\tilde{S}_n\}_{n\geq1}=\{\tilde{X}_1+\cdots+\tilde{X}_n\}_{n\geq1}$ that inserts memory and echo into an ordinary random walk (ORW) with i.i.d. steps, $X_1+\cdots+X_n$. The RWES is…

Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale…

In this paper we revise the theory of turnpikes in discounted Markov decision processes, prove the turnpike theorem for the undiscounted model and apply the results to the specific random walk.

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…

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with…

We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…

Graph vertex embeddings based on random walks have become increasingly influential in recent years, showing good performance in several tasks as they efficiently transform a graph into a more computationally digestible format while…

We are interested in the randomly biased random walk on the supercritical Galton--Watson tree. Our attention is focused on a slow regime when the biased random walk $(X_n)$ is null recurrent, making a maximal displacement of order of…

For any recurrent random walk (S_n)_{n>0} on R, there are increasing sequences (g_n)_{n>0} converging to infinity for which (g_n S_n)_{n>0} has at least one finite accumulation point. For one class of random walks, we give a criterion on…

We consider in this article an Elephant Random Walk evolving in the plane. Specifically, this is a reinforced stochastic process in which the $n$th step is given by a random rotation of one of the previous steps chosen uniformly at random.…

We study the condensation regime of the finite reversible inclusion process, i.e., the inclusion process on a finite graph $S$ with an underlying random walk that admits a reversible measure. We assume that the random walk kernel is…