Related papers: Anomalous diffusion in random-walks with memory-in…
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…
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 the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
We study several lattice random walk models with stochastic resetting to previously visited sites which exhibit a phase transition between an anomalous diffusive regime and a localization regime where diffusion is suppressed. The localized…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random walk model with long range memory for which not only the mean square displacement (MSD) can be obtained exactly in the…
We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which…
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of…
The problem of a random walk in a disordered media is mapped into a model of a random walk with memory. The latter model, as opposed to the former one, does not make reference to a particular realization of the disorder. The equivalence of…
We consider the problem of diffusion with stochastic resetting in a population of random walks where the diffusion coefficient is not constant, but behaves as a power-law of the average resetting rate of the population. Resetting occurs…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
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…
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…
The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
The concept of random walk, in which particles or waves undergo multiple collisions with the microscopic constituents of a surrounding medium, is central to understanding diffusive transport across many research areas. However, this…
We study a random walk model in which the jumping probability to a site is dependent on the number of previous visits to the site, as a model of the mobility with memory. To this end we introduce two parameters called the memory parameter…