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We consider the dynamical evolution of a Brownian particle undergoing stochastic resetting, meaning that after random periods of time it is forced to return to the starting position. The intervals after which the random motion is stopped…
Resetting, in which a system is regularly returned to a given state after a fixed or random duration, has become a useful strategy to optimize the search performance of a system. While earlier theoretical frameworks focused on instantaneous…
Stochastic resetting has attracted significant attention in recent years due to its wide-ranging applications across physics, biology, and search processes. In most existing studies, however, resetting events are governed by an external…
We consider random walkers searching for a target in a bounded one-dimensional heterogeneous environment, in the interval $[0,L]$, where diffusion is described by a space-dependent diffusion coefficient $D(x)$. Boundary conditions are…
We consider diffusion under stochastic resetting to the origin in one dimension and compute the mean time to find both of two targets placed either side of the origin. A surprising result is that increasing the distance between two targets…
One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…
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…
In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a…
Resetting has been shown to reduce the completion time for a stochastic process, such as the first passage time for a diffusive searcher to find a target. The time between two consecutive resetting events is drawn from a waiting time…
Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in…
We introduce a new class of first passage time optimization driven by threshold resetting, inspired by many natural processes where crossing a critical limit triggers failure, degradation or transition. In here, search agents are…
We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known…
Diffusion with stochastic resetting has recently emerged as a powerful modeling tool with a myriad of potential applications. Here, we study local time in this model, covering situations of free and biased diffusion with, and without, the…
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…
In this paper we use asymptotic analysis to determine the steady-state mean number of resources in each of $N$ small interior targets within a three-dimensional bounded domain. The accumulation of resources is based on multiple rounds of…
We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the…
In this paper we consider diffusion in a domain $\Omega$ containing a partially absorbing target $\calM$ with position and occupation time resetting. The occupation time $A_t$ is a Brownian functional that determines the amount of time that…
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of…
We study a class of stochastic resetting (SR) processes in which a diffusing particle alternates between free motion and confinement by an externally controlled potential. When the particle is recaptured, it undergoes a return trajectory…
The cost of stochastic resetting is considered within the context of a discrete random walk model. In addition to standard stochastic resetting, for which a reset occurs with a certain probability after \emph{each} step, we introduce a…