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Animal telemetry data are often analysed with discrete time movement models assuming rotation in the movement. These models are defined with equidistant distant time steps. However, telemetry data from marine animals are observed…

Quantitative Methods · Quantitative Biology 2018-06-25 Christoffer Moesgaard Albertsen

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

Probability · Mathematics 2026-04-28 Hubert Woszczek , Marek A. Teuerle , Agnieszka Wyłomańska

In this paper, we conduct a literature review of laws of motion based on stochastic search strategies which are mainly focused on exploring highly dynamic environments. In this regard, stochastic search strategies represent an interesting…

Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this…

Applications · Statistics 2017-05-19 Alison Parton , Paul G. Blackwell

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…

Statistical Mechanics · Physics 2015-05-14 Gleb Oshanin , Katja Lindenberg , Horacio S Wio , Sergei Burlatsky

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…

Statistical Mechanics · Physics 2012-02-28 V. Tejedor , R. Voituriez , O. Bénichou

Biologically inspired strategies have long been adapted to swarm robotic systems, including biased random walks, reaction to chemotactic cues and long-range coordination. In this paper we apply analysis tools developed for modeling…

Both resources in the natural environment and concepts in a semantic space are distributed "patchily", with large gaps in between the patches. To describe people's internal and external foraging behavior, various random walk models have…

Machine Learning · Computer Science 2017-10-17 Jian-Qiao Zhu , Adam N. Sanborn , Nick Chater

We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…

Probability · Mathematics 2017-09-12 Mihai Gradinaru , Tristan Haugomat

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…

Applications · Statistics 2025-10-07 Théo Michelot , Ephraim M. Hanks

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…

Statistical Mechanics · Physics 2014-12-02 Giampaolo Cristadoro , Thomas Gilbert , Marco Lenci , David P. Sanders

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…

Populations and Evolution · Quantitative Biology 2015-05-19 Denis Boyer , Peter D. Walsh

L\'evy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of…

Statistical Mechanics · Physics 2020-07-01 Pengbo Xu , Tian Zhou , Ralf Metzler , Weihua Deng

Scaling mobility patterns have been widely observed for animals. In this paper, we propose a deterministic walk model to understand the scaling mobility patterns, where walkers take the least-action walks on a lattice landscape and prey.…

Data Analysis, Statistics and Probability · Physics 2015-05-20 Xiao-Pu Han , Tao Zhou , Bing-Hong Wang

We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with L\'evy search based on…

Statistical Mechanics · Physics 2017-11-01 V. V. Palyulin , Vladimir N. Mantsevich , R. Klages , R. Metzler , A. V. Chechkin

Target shape, not just size, plays a pivotal role in determining detectability during random search. We analyze intermittent L\'evy walks in three dimensions, and mathematically prove that the widely observed Cauchy strategy (L\'evy…

Data Structures and Algorithms · Computer Science 2026-03-12 Matteo Stromieri , Emanuele Natale , Amos Korman

Social behavior across animal species ranges from simple pairwise interactions to thousands of individuals coordinating goal-directed movements. Regardless of the scale, these interactions are governed by the interplay between multimodal…

Neurons and Cognition · Quantitative Biology 2024-08-06 Sarah Josephine Stednitz , Andrew Lesak , Adeline L Fecker , Peregrine Painter , Phil Washbourne , Luca Mazzucato , Ethan K Scott

Quantifying and comparing patterns of dynamical ecological systems require averaging over measurable quantities. For example, to infer variation in movement and behavior, metrics such as step length and velocity are averaged over large…

Populations and Evolution · Quantitative Biology 2022-05-24 Ohad Vilk , Yotam Orchan , Motti Charter , Nadav Ganot , Sivan Toledo , Ran Nathan , Michael Assaf

Understanding species-habitat associations is fundamental to ecological sciences and for species conservation. Consequently, various statistical approaches have been designed to infer species-habitat associations. Due to their conceptual…

We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as…

Statistical Mechanics · Physics 2015-05-19 Ihor Lubashevsky , Andreas Heuer , Rudolf Friedrich , Ramil Usmanov