Related papers: Random walks with asymmetric time delays
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time…
Biomechanics and human movement research often involves measuring multiple kinematic or kinetic variables regularly throughout a movement, yielding data that present as smooth, multivariate, time-varying curves and are naturally amenable to…
We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
The patterns of motion of mobile agents has received recently wide attention in the literature. There is a number of recent studies centered around the motion behavior of many agents ranging from albatrosses to human beings. Special…
We prove a quenched functional central limit theorem for a one-dimensional random walk driven by a simple symmetric exclusion process. This model can be viewed as a special case of the random walk in a balanced random environment, for which…
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an…
We study the influence of motion on the emergence of synchronization in a metapopulation of random walkers moving on a heterogeneous network and subject to Kuramoto interactions at the network nodes. We discover a novel mechanism of…
Many stochastic systems in physics and biology are investigated by recording the two-dimensional (2D) positions of a moving test particle in regular time intervals. The resulting sample trajectories are then used to induce the properties of…
Let $G$ be a finitely generated group equipped with a finite symmetric generating set and the associated word length function $|\cdot |$. We study the behavior of the probability of return for random walks driven by symmetric measures $\mu$…
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…
Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…
We show that asymmetric time-continuous discrete random walks can display bistability for equal values of Jauslin's shifting parameters. The bistability becomes more pronounced at increased asymmetry parameter
We study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
We study a natural construction of a general class of inhomogeneous quantum walks (namely walks whose transition probabilities depend on position). Within the class we analyze walks that are periodic in position and show that, depending on…
For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks…
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…
Random walk subject to random drive has been extensively employed as a model for physical and biological processes. While equilibrium statistical physics has yielded significant insights into the distributions of dynamical fixed points of…
This paper provides a detailed description for the asymptotics of exponential functionals of random walks with light/heavy tails. We give the convergence rate based on the key observation that the asymptotics depends on the sample paths…
We study continuous-time (variable speed) random walks in random environments on $\mathbb{Z}^d$, $d\ge2$, where, at time $t$, the walk at $x$ jumps across edge $(x,y)$ at time-dependent rate $a_t(x,y)$. The rates, which we assume stationary…