Related papers: Optimizing persistent random searches
We determine the full distribution and moments of the first passage time for a wide class of stochastic search processes in the limit of frequent stochastic resetting. Our results apply to any system whose short-time behavior of the search…
We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect…
We investigate a stochastic search process in one, two, and three dimensions in which $N$ diffusing searchers that all start at $x_0$ seek a target at the origin. Each of the searchers is also reset to its starting point, either with rate…
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…
The statistics of first-passage times of random walks to target sites has proved to play a key role in determining the kinetics of space exploration in various contexts. In parallel, the number of distinct sites visited by a random walker…
We focus on the problem of performing random walks efficiently in a distributed network. Given bandwidth constraints, the goal is to minimize the number of rounds required to obtain a random walk sample. We first present a fast sublinear…
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
The cover time is defined as the time needed for a random walker to visit every site of a confined domain. Here, we focus on persistent random walks, which provide a minimal model of random walks with short range memory. We derive the exact…
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…
The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a…
Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a…
We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…
The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…
Random walks are gaining much attention from the networks research community. They are the basis of many proposals aimed to solve a variety of network-related problems such as resource location, network construction, nodes sampling, etc.…
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…
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the…
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT)…
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
Random walks can be used to search complex networks for a desired resource. To reduce search lengths, we propose a mechanism based on building random walks connecting together partial walks (PW) previously computed at each network node.…
Agents searching for a target can improve their efficiency by memorizing where they have already been searching or by cooperating with other searchers and using strategies that benefit from collective effects. This chapter reviews such…