Related papers: Probability distribution of the sizes of largest e…

In this paper we analyse random walk on a fractal structure, specifi- cally fractal curves, using the recently develped calculus for fractal curves. We consider only unbiased random walk on the fractal stucture and find out the…

We investigate a L\'evy-Walk alternating between velocities $\pm v_0$ with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic…

We show that the largest disc covered by a simple random walk (SRW) on $\mathbb{Z}^2$ after n steps has radius n^{1/4+o(1)}, thus resolving an open problem of R\'{e}v\'{e}sz [Random Walk in Random and Non-Random Environments (1990) World…

We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…

Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…

We offer theoretical explanations for some recent observations in numerical simulations of quantum random walks (QRW). Specifically, in the case of a QRW on the line with one particle (walker) and two entangled coins, we explain the…

We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…

Consider a nearest neighbor random walk on the two-dimensional integer lattice, where each vertex is initially labeled either `H' or `V', uniformly and independently. At each discrete time step, the walker resamples the label at its current…

We construct examples of a random walk with pairwise-independent steps which is almost-surely bounded, and for any $m$ and $k$ a random walk with $k$-wise independent steps which has no stationary distribution modulo $m$.

We prove distributional limit theorems for the length of the largest convex minorant of a one-dimensional random walk with independent identically distributed increments. Depending on the increment law, there are several regimes with…

We provide a uniform framework to compute the exact distribution of the number of minima/maxima in three different random walk landscape models in one dimension. The landscape is generated by the trajectory of a discrete-time continuous…

Probability distributions of human displacements has been fit with exponentially truncated L\'evy flights or fat tailed Pareto inverse power law probability distributions. Thus, people usually stay within a given location (for example, the…

The propagation of light that undergoes multiple-scattering by resonant atomic vapor can be described as a L\'evy flight. L\'evy flight is a random walk with heavy tailed step-size (r) distribution, decaying asymptotically as $P(r)\sim…

Unlike classical simple random walks, one-dimensional random walks in random environments (RWRE) are known to have a wide array of potential limiting distributions. Under certain assumptions, however, it is known that CLT-like limiting…

A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is $\ell$ is taken as…

When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…

We study the excited random walk, in which a walk that is at a site that contains cookies eats one cookie and then hops to the right with probability p and to the left with probability q=1-p. If the walk hops onto an empty site, there is no…

We perform a thorough analysis of the survival probability of symmetric random walks with stochastic resetting, defined as the probability for the walker not to cross the origin up to time $n$. For continuous symmetric distributions of step…

We study the large deviations of one-dimensional excited random walks. We prove a large deviation principle for both the hitting times and the position of the random walk and give a qualitative description of the respective rate functions.…

We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…