Related papers: Urn-related random walk with drift $\rho x^{\alpha…
When random walks on a square lattice are biased horizontally to move solely to the right, the probability distribution of their algebraic area can be exactly obtained. We explicitly map this biased classical random system on a non…
The effect of unitary noise on the discrete one-dimensional quantum walk is studied using computer simulations. For the noiseless quantum walk, starting at the origin (n=0) at time t=0, the position distribution Pt(n) at time t is very…
Random walkers characterized by random positions and random velocities lead to normal diffusion. A random walk was originally proposed by Einstein to model Brownian motion and to demonstrate the existence of atoms and molecules. Such a…
We study an unbiased, discrete time random walk on the nonnegative integers, with the origin absorbing. The process has a history-dependent step length: the walker takes steps of length v while in a region which has been visited before, and…
In this paper we consider finitary symmetric random walks on groups. We construct new possible asymptotics for the drift. We show that the drift can be very close to linear ant yet sublinear. We also give estimates for entropy growth of…
We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z^2 starting on the boundary exits A at another specified boundary point. The estimates are uniform over all domains of a given inradius.…
We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…
We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…
We prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under…
An excited random walk is a non-Markovian extension of the simple random walk, in which the walk's behavior at time $n$ is impacted by the path it has taken up to time $n$. The properties of an excited random walk are more difficult to…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…
A new proof is given for the formula for the expected return time of a random walk on a graph. This proof makes use of known relationships between electric resistance and random walks.
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
In this work we study asymptotic properties of a long range memory random walk known as elephant random walk. First we prove recurrence and positive recurrence for the elephant random walk. Then, we establish the transience regime of the…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…
We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
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,…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…