Related papers: Emergence of L\'evy walks from second order stocha…
What is the most efficient search strategy for the random located target sites subject to the physical and biological constraints? Previous results suggested the L\'evy flight is the best option to characterize this optimal problem,…
L\'evy walks are found in the migratory behaviour patterns of various organisms, and the reason for this phenomenon has been much discussed. We use simulations to demonstrate that learning causes the changes in confidence level during…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
L\'evy Flights are paradigmatic generalised random walk processes, in which the independent stationary increments---the "jump lengths"---are drawn from an $\alpha$-stable jump length distribution with long-tailed, power-law asymptote. As a…
We study analytically an intermittent search process in one dimension. There is an immobile target at the origin and a searcher undergoes a discrete time jump process starting at $x_0\geq0$, where successive jumps are drawn independently…
We consider trawl processes, which are stationary and infinitely divisible stochastic processes and can describe a wide range of statistical properties, such as heavy tails and long memory. In this paper, we develop the first…
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…
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…
Stochastic resetting is a protocol of starting anew, which can be used to facilitate the escape kinetics. We demonstrate that restarting can accelerate the escape kinetics from a finite interval restricted by two absorbing boundaries also…
A Levy walk is a non-Markovian stochastic process in which the elementary steps of the walker consist of motion with constant speed in randomly chosen directions and for a random period of time. The time of flight is chosen from a…
A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…
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…
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 explore a two-step optimization problem in random environments, the so-called restaurant-coffee shop problem, where a walker aims at visiting the nearest and better restaurant in an area and then move to the nearest and better…
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 consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function…
The spectral theory of random walks on networks of arbitrary topology can be readily extended to study random walks and L\'evy flights subject to resetting on these structures. When a discrete-time process is stochastically brought back…
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in…
Animals foraging alone are hypothesized to optimize the encounter rates with resources through L\'evy walks. However, the issue of how the interactions between multiple foragers influence their search efficiency is still not completely…
Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on…