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L\'evy walks are random walk processes whose step-lengths follow a long-tailed power-law distribution. Due to their abundance as movement patterns of biological organisms, significant theoretical efforts have been devoted to identifying the…
The L\'evy hypothesis states that inverse square L\'evy walks are optimal search strategies because they maximise the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret…
The L\'evy flight foraging hypothesis states that organisms must have evolved adaptations to exploit L\'evy walk search strategies. Indeed, it is widely accepted that inverse square L\'evy walks optimize the search efficiency in foraging…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
It is widely accepted that inverse square L\'evy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets when the search restarts in the vicinity of the…
Levy flights are known to be optimal search strategies in the particular case of revisitable targets. In the relevant situation of non revisitable targets, we propose an alternative model of bidimensional search processes, which explicitly…
The Levy walk in which the frequency of occurrence of step lengths follows a power-law distribution, can be observed in the migratory behavior of organisms at various levels. Levy walks with power exponents close to 2 are observed, and the…
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest…
Foraging is a complex spatio-temporal process which is often described with stochastic models. Two particular ones, L\'evy walks (LWs) and intermittent search (IS), became popular in this context. Researchers from the two communities, each…
Search strategies based on random walk processes with long-tailed jump length distributions (Levy walks) on the one hand and intermittent behavior switching between local search and ballistic relocation phases on the other, have been…
An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study…
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the…
Autonomous robots are commonly tasked with the problem of area exploration and search for certain targets or artifacts of interest to be tracked. Traditionally, the problem formulation considered is that of complete search and thus -…
We present a simple model to study L\'{e}vy-flight foraging in a finite landscape with countable targets. In our approach, foraging is a step-based exploratory random search process with a power-law step-size distribution $P(l) \propto…
Motivated by the L\'evy foraging hypothesis -- the premise that various animal species have adapted to follow L\'evy walks to optimize their search efficiency -- we study the parallel hitting time of L\'evy walks on the infinite…
In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…
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,…
We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…