Related papers: Return Probabilities for the Reflected Random Walk…
In this paper, we show that reflecting Brownian motion in any bounded domain D can be approximated, as $k\to\infty$, by simple random walks on "maximal connected" subsets of $(2^{-k}\mathbb{Z}^d)\cap D$ whose filled-in interiors are inside…
It is classical to approximate the distribution of fractional Brownian motion by a renormalized sum $ S_n $ of dependent Gaussian random variables. In this paper we consider such a walk $ Z_n $ that collects random rewards $ \xi_j $ for $ j…
We consider the range of random walks up to time n, R_n, on graphs satisfying a uniform condition. This condition is characterized by potential theory. Not only all vertex transitive graphs but also many non-regular graphs satisfy the…
Let $G=(V,E)$ be a $d$-regular graph on $n$ vertices and let $\mu_0$ be a probability measure on $V$. The act of moving to a randomly chosen neighbor leads to a sequence of probability measures supported on $V$ given by $\mu_{k+1} = A…
We consider a one-dimensional random walk $S_n$ with i.i.d. increments with zero mean and finite variance. We study the asymptotic expansion for the tail distribution $\mathbf P(\tau_x>n)$ of the first passage times…
We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as…
We consider random walks X_n in Z+, obeying a detailed balance condition, with a weak drift towards the origin when X_n tends to infinity. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional…
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…
Several well-known results from the random matrix theory, such as Wigner's law and the Marchenko--Pastur law, can be interpreted (and proved) in terms of non-backtracking walks on a certain graph. Orthogonal polynomials with respect to the…
Let $G$ be a finitely generated group of polynomial volume growth equipped with a word-length $|\cdot|$. The goal of this paper is to develop techniques to study the behavior of random walks driven by symmetric measures $\mu$ such that, for…
Consider $(1,2)$ random walk in random environment $\{X_n\}_{n\ge0}.$ In each step, the walk jumps at most a distance $2$ to the right or a distance $1$ to the left. For the walk transient to the right, it is proved that almost surely…
Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…
Random walk is an explainable approach for modeling natural processes at the molecular level. The Random Permutation Set Theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer Theory.…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
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 consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset which is invariant by the walk has zero or infinite…
We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the…
We study an inverse problem on a finite connected graph G = (X, E), on whose vertices a conductivity {\gamma} is defined. Our data consists in a sequence of partial observations of a fractional random walk on G. The observations are partial…
This paper deals with different models of random walks with a reinforced memory of preferential attachment type. We consider extensions of the Elephant Random Walk introduced by Sch\"utz and Trimper [2004] with a stronger reinforcement…
We study a self-attractive random walk such that each trajectory of length $N$ is penalised by a factor proportional to $\exp ( - |R_N|)$, where $R_N$ is the set of sites visited by the walk. We show that the range of such a walk is close…