Related papers: A random walk model to study the cycles emerging f…
The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed…
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied…
In recent years, we have seen scientists attempt to model and explain human dynamics and, in particular, human movement. Many aspects of our complex life are affected by human movements such as disease spread and epidemics modeling, city…
We prove a quenched invariance principle for a class of random walks in random environment on $\mathbb{Z}^d$, where the walker alters its own environment. The environment consists of an outgoing edge from each vertex. The walker updates the…
World models enable agents to plan within imagined environments by predicting future states conditioned on past observations and actions. However, their ability to plan over long horizons is limited by the effective memory span of the…
Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…
We study a simple model of a foraging animal that modifies the substrate on which it moves. This substrate provides its only resource, and the forager manage it by taking a limited portion at each visited site. The resource recovers its…
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent…
In this paper we extend the concept of persistence, well defined for classical stochastic dynamics, to the context of quantum dynamics. We demonstrate the idea via quantum random walk and a successive measurement scheme, where persistence…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
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 $\alpha>d$,…
The monkey walk is a stochastic process defined as the trajectory of a walker that moves on $\mathbb R^d$ according to a Markovian generator, except at some random "relocation" times at which it jumps back to its position at a time sampled…
We study a random walk on $\mathbb{Z}$ which evolves in a dynamic environment determined by its own trajectory. Sites flip back and forth between two modes, $p$ and $q$. $R$ consecutive right jumps from a site in the $q$-mode are required…
A mass of traces of human activities show diverse dynamic patterns. In this paper, we comprehensively investigate the dynamic pattern of human attention defined by the quantity of interests on subdisciplines in an online academic…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…
We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. We derive exact results for the probability of visiting a given number of sites and develop a…
In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…
We study a discrete random walk on a one-dimensional finite lattice, where each state has different probabilities to move one step forward, backward, staying for a moment or being absorbed. We obtain expected number of arrivals and expected…
Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for…