Related papers: The Sokoban Random Walk: A Trapping Perspective
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…
We consider the phase transition induced by compressing a self-avoiding walk in a slab where the walk is attached to both walls of the slab in two and three dimensions, and the resulting phase once the polymer is compressed. The process of…
We investigate the dynamic relaxation of random walks on temporal networks by focusing in the recently proposed activity driven model [Perra \textit{et al.} Sci. Rep. srep00469 (2012)]. For realistic activity distributions with a power-law…
We study various models of independent particles hopping between energy `traps' with a density of energy barriers $\rho(E)$, on a $d$ dimensional lattice or on a fully connected lattice. If $\rho(E)$ decays exponentially, a true dynamical…
We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method…
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…
The sampling of the configuration space in diffusion Monte Carlo (DMC) is done using walkers moving randomly. In a previous work on the Hubbard model [\href{https://doi.org/10.1103/PhysRevB.60.2299}{Assaraf et al.~Phys.~Rev.~B \textbf{60},…
Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…
We study the gambler's ruin problem for the Elephant Random Walk, focusing on escape time from a symmetric interval of the form $\{-N, \ldots, N\}$. As our main result, we derive tight exponential bounds for the tail of this escape time. We…
We consider a discrete-time random walk on a one-dimensional lattice with space and time-dependent random jump probabilities, known as the Beta random walk. We are interested in the probability that, for a given realization of the jump…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time…
We study experimentally statistical properties of the opening times of knots in vertically vibrated granular chains. Our measurements are in good qualitative and quantitative agreement with a theoretical model involving three random walks…
Consider a random walk in random environment on a supercritical Galton--Watson tree, and let $\tau_n$ be the hitting time of generation $n$. The paper presents a large deviation principle for $\tau_n/n$, both in quenched and annealed cases.…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
We present a class of stochastic processes in which the large deviation functions of time-integrated observables exhibit singularities that relate to dynamical phase transitions of trajectories. These illustrative examples include Brownian…
Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized around their initial position. The existence of eigenvalues of time evolution operators is a necessary and…
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.…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…