# Inverse Square Lévy Walks are not Optimal Search Strategies for d≥2.

@article{Levernier2020InverseSL, title={Inverse Square L{\'e}vy Walks are not Optimal Search Strategies for d≥2.}, author={Nicolas Levernier and Johannes Textor and Olivier B{\'e}nichou and Rapha{\"e}l Voituriez}, journal={Physical review letters}, year={2020}, volume={124 8}, pages={ 080601 } }

The Lévy hypothesis states that inverse square Lévy walks are optimal search strategies because they maximize the encounter rate with sparse, randomly distributed, replenishable targets. It has served as a theoretical basis to interpret a wealth of experimental data at various scales, from molecular motors to animals looking for resources, putting forward the conclusion that many living organisms perform Lévy walks to explore space because of their optimal efficiency. Here we provide…

## 17 Citations

Intermittent inverse-square Lévy walks are optimal for finding targets of all sizes

- Computer Science, BiologyScience Advances
- 2021

It is proved that in finite two-dimensional terrains, the inverse-square Lévy walk strategy is extremely efficient at finding sparse targets of arbitrary size and shape.

Search via Parallel Lévy Walks on Z

- 2021

Motivated by the Lévy foraging hypothesis – the premise that various animal species have adapted to follow Lévy walks to optimize their search efficiency – we study the parallel hitting time of Lévy…

Functional advantages of Lévy walks emerging near a critical point

- Biology, Computer Science
- 2020

This work modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information and suggested that LÉvy walks could change movement trajectories based on the magnitude of environmental stimuli.

Functional advantages of Lévy walks emerging near a critical point

- Medicine, Computer ScienceProceedings of the National Academy of Sciences
- 2020

It is shown that there could be functional advantages associated with Lévy walks emerging near a critical point, including a large dynamic range to stimuli and highly flexible switching between exploitation and exploration and empirically confirmed these functional advantages by analyzing movement trajectories of freely moving Drosophila larvae.

F UNCTIONAL ADVANTAGES OF L ÉVY WALKS EMERGING NEAR A CRITICAL

- 2020

A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their…

Efficiency functionals for the Lévy flight foraging hypothesis

- 2021

We consider a forager diffusing via a fractional heat equation and we introduce several efficiency functionals whose optimality is discussed in relation to the Lévy exponent of the evolution…

Extreme statistics of superdiffusive Levy flights and every other Levy subordinate Brownian motion

- Mathematics, Physics
- 2021

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…

Search via Parallel Lévy Walks on ${\mathbb Z}^2$

- Computer Science
- 2020

This work studies the parallel hitting time of Levy walks on the infinite two-dimensional grid, and proposes a surprisingly simple and effective parallel search strategy, which achieves optimal search time (modulo polylogarithmic factors) among all possible algorithms (even centralized ones that know $k).

Environment-imposed constraints make Brownian walkers efficient searchers

- Computer Science
- 2020

The results strongly suggest that observed patterns of movement of CD8 T cells are likely to result from a combination of a cell-intrinsic movement program, physical constraints imposed by the environmental structures, and other environmental cues.

Description of an ecological niche for a mixed local/nonlocal dispersal: An evolution equation and a new Neumann condition arising from the superposition of Brownian and Lévy processes

- Mathematics
- 2021

Abstract We propose here a motivation for a mixed local/nonlocal problem with a new type of Neumann condition. Our description is based on formal expansions and approximations. In a nutshell, a…

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