Related papers: Excited random walks with non-nearest neighbor ste…

We consider a family of one-dimensional self interacting walks whose dynamics characterized by a monotone weight function $w$ on $\mathbb{N}\cup \{0\}$. The weight function takes the form $w(n) = (1 + 2^p Bn^{-p} + O(n^{-1-\kappa}))^{-1}$,…

Deterministic walks over a random set of points in one and two dimensions (d=1,2) are considered. Points (``cities'') are randomly scattered in R^d following a uniform distribution. A walker (a ``tourist''), at each time step, goes to the…

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…

We conjecture the expected value of random walks with anti-correlated steps to be exactly 1. We support this conjecture with 2 plausibility arguments and experimental data. The experimental analysis includes the computation of the expected…

Let $N$ and $M$ be positive integers satisfying $1\le M\le N$, and let $0<p_0<p_1<1$. Define a process $\{X_n\}_{n=0}^\infty$ on $\mathbb{Z}$ as follows. At each step, the process jumps either one step to the right or one step to the left,…

A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…

Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \in \{1,2\}$ but transient if $d \geq 3$. Once spatial homogeneity is…

When the memory parameter of the elephant random walk is above a critical threshold, the process becomes superdiffusive and, once suitably normalised, converges to a non-Gaussian random variable. In a recent paper by the three first…

Consider a sequence {X(i,0) : i = 1, ..., n} of i.i.d. random variables. Associate to each X(i,0) an independent mean-one Poisson clock. Every time a clock rings replace that X-variable by an independent copy. In this way, we obtain i.i.d.…

For positive integers $\alpha$ and $\beta$, we define an $(\alpha,\beta)$-walk to be any sequence of positive integers satisfying $w_{k+2}=\alpha w_{k+1}+\beta w_k$. We say that an $(\alpha,\beta)$-walk is $n$-slow if $w_s=n$ with $s$ as…

On a locally compact group $E$ with countable base, we consider a random walk $X$ that has a unique (up to a positive factor) $r$-invariant measure for some $r>0$. Under some weak conditions on the measure, there is a unique continuous…

Simple random walks on a partially directed version of $\mathbb{Z}^2$ are considered. More precisely, vertical edges between neighbouring vertices of $\mathbb{Z}^2$ can be traversed in both directions (they are undirected) while horizontal…

The balanced excited random walk, introduced by Benjamini, Kozma and Schapira in $2011$, is defined as a discrete time stochastic process in $\mathbb Z^d$, depending on two integer parameters $1\le d_1,d_2\le d$, which whenever it is at a…

We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which…

Consider an arbitrary transient random walk on $\Z^d$ with $d\in\N$. Pick $\alpha\in[0,\infty)$ and let $L_n(\alpha)$ be the spatial sum of the $\alpha$-th power of the $n$-step local times of the walk. Hence, $L_n(0)$ is the range,…

A pair of random walks $(R,S)$ on the vertices of a graph $G$ is {\it successful} if two tokens can be scheduled (moving only one token at a time) to travel along $R$ and $S$ without colliding. We consider questions related to P. Winkler's…

We analyze the recurrence probability (P\'olya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localisation of quantum…

We study graph-theoretic properties of the trace of a random walk on a random graph. We show that for any $\varepsilon>0$ there exists $C>1$ such that the trace of the simple random walk of length $(1+\varepsilon)n\ln{n}$ on the random…

We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…

We examine a system of interacting random walks with leftward drift on $\mathbb{Z}$, which begins with a single active particle at the origin and some distribution of inactive particles on the positive integers. Inactive particles become…