Related papers: Random walks on generalized visible lattice points
Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…
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 prove log-concavity of exit probabilities of lattice random walks in certain planar regions.
The exact mean time between encounters of a given particle in a system consisting of many particles undergoing random walks in discrete time is calculated, on both regular and complex networks. Analytical results are obtained both for…
This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the…
We establish the existence of generalized Busemann functions and Gibbs-Dobrushin-Landford-Ruelle measures for a general class of lattice random walks in random potential with finitely many admissible steps. This class encompasses directed…
In this paper, we investigate the quest for a single target, that remains fixed in a lattice, by a set of independent walkers. The target exhibits a fluctuating behavior between trap and ordinary site of the lattice, whereas the walkers…
We consider deterministic walks on square, triangular and hexagonal two dimensional lattices. In each case, there is a scatterer at every site that can be in one of two states that force the walker to turn either to his/her immediate right…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Real networks are often dynamic. In response to it, analyses of algorithms on {\em dynamic networks} attract more and more attentions in network science and engineering. Random walks on dynamic graphs also have been investigated actively in…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.
The study of random walks has increasingly been popular across diverse disciplines such as statistics, mathematics, quantum physics, where they are used to model paths consisting of successive random steps in a mathematical space. A…
We consider a random walk on integers where at the first visits to a site the walker gets a positive drift, but where after a certain number of visits the walker gets a negative drift. We prove that the walker is almost surely transient to…
There is a close connection between intersections of Brownian motion paths and percolation on trees. Recently, ideas from probability on trees were an important component of the multifractal analysis of Brownian occupation measure, in joint…
In this work, we are interested in the set of visited vertices of a tree $\mathbb{T}$ by a randomly biased random walk $\mathbb{X}:=(X_n,n \in \mathbb{N})$. The aim is to study a generalized range, that is to say the volume of the trace of…
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 present a probabilistic theory of random walks in turbid media with non-scattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics and void spacings can be…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…