Related papers: Sign-time distribution for a random walker with a …
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
In this note, by an elementary use of Girsanov's transform we show that the exit time for either a biased random walk or a drifted Brownian motion on a symmetric interval is stochastically monotone with respect to the drift parameter. In…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method…
The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…
It is well known that many real world networks have the power-law degree distribution (scale-free property). However there are no rigorous results for continuous-time quantum walks on such realistic graphs. In this paper, we analyze…
We consider a centered random walk with finite variance and investigate the asymptotic behaviour of the probability that the area under this walk remains positive up to a large time $n$. Assuming that the moment of order $2+\delta$ is…
We introduce a cover time problem for random walks on dynamic graphs in which the graph expands in time and the walker moves at random times. Time to cover all nodes and number of returns to original states are analyzed in resulting model.
We study a class of nearest-neighbor discrete time integer random walks introduced by Zerner, the so called multi-excited random walks. The jump probabilities for such random walker have a drift to the right whose intensity depends on a…
We obtain expected number of arrivals, absorption probabilities and expected time until absorption for an asymmetric discrete random walk on a graph in the presence of multiple function barriers. On each edge of the graph and in each vertex…
We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
We prove an invariance principle for continuous-time random walks in a dynamically averaging environment on $\mathbb Z$. In the beginning, the conductances may fluctuate substantially, but we assume that as time proceeds, the fluctuations…
We derive diffusion constants and martingales for senile random walks with the help of a time-change. We provide direct computations of the diffusion constants for the time-changed walks. Alternatively, the values of these constants can be…
We study the transmission of random walkers through a finite-size inhomogeneous material with a quenched, long-range correlated distribution of scatterers. We focus on a finite one-dimensional structure where walkers undergo random…
This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its…
Asymptotic estimates of the hitting distribution of a long segment on the real axis for two dimensional random walks on ${\bf Z}^2$ of zero mean and finite variances are obtained: some are general and exhibit its apparent similarity to the…
We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over…