Lévy flights and Lévy walks revisited

2007 ◽  
pp. 15-34 ◽  
Author(s):  
G. Zumofen ◽  
J. Klafter ◽  
M. F. Shlesinger
Keyword(s):  
Lévy Flights ◽  
Lévy Walks ◽  
Levy Flights

Lévy Walks Versus Lévy Flights

1986 ◽  
pp. 279-283 ◽  
Author(s):  
Michael F. Shlesinger ◽  
Joseph Klafter
Keyword(s):  
Lévy Flights ◽  
Lévy Walks ◽  
Levy Flights

scholarly journals On the Critical Delays of Mobile Networks Under Lévy Walks and Lévy Flights

2013 ◽  
Vol 21 (5) ◽  
pp. 1621-1635 ◽  
Author(s):  
Kyunghan Lee ◽  
Yoora Kim ◽  
Song Chong ◽  
Injong Rhee ◽  
Yung Yi ◽  
...  
Keyword(s):  
Mobile Networks ◽  
Lévy Flights ◽  
Lévy Walks ◽  
Levy Flights

scholarly journals Lévy flights versus Lévy walks in bounded domains

2017 ◽  
Vol 95 (5) ◽  
Author(s):  
Bartłomiej Dybiec ◽  
Ewa Gudowska-Nowak ◽  
Eli Barkai ◽  
Alexander A. Dubkov
Keyword(s):  
Bounded Domains ◽  
Lévy Flights ◽  
Lévy Walks ◽  
Levy Flights

scholarly journals First passage and first hitting times of Lévy flights and Lévy walks

2019 ◽  
Vol 21 (10) ◽  
pp. 103028 ◽  
Author(s):  
Vladimir V Palyulin ◽  
George Blackburn ◽  
Michael A Lomholt ◽  
Nicholas W Watkins ◽  
Ralf Metzler ◽  
...  
Keyword(s):  
Hitting Times ◽  
First Passage ◽  
Lévy Flights ◽  
Lévy Walks ◽  
Levy Flights ◽  
First Hitting Times

scholarly journals Extending Lévy search theory from one to higher dimensions: Lévy walking favours the blind

2015 ◽  
Vol 471 (2179) ◽  
pp. 20150123 ◽  
Author(s):  
A. M. Reynolds
Keyword(s):  
T Cells ◽  
Three Dimensional ◽  
Search Theory ◽  
Three Dimensions ◽  
Lévy Flight ◽  
Lévy Flights ◽  
Levy Flight ◽  
Diverse Range ◽  
Lévy Walks ◽  
Levy Flights

A diverse range of organisms, including T cells, E. coli , honeybees, sharks, turtles, bony fish, jellyfish, wandering albatrosses and even human hunter–gatherers have movement patterns that can be approximated by Lévy walks (LW; sometimes called Lévy flights in the biological and ecological literature). These observations lend support to the ‘Lévy flight foraging hypothesis’ which asserts that natural selection should have led to adaptations for Lévy flight foraging, because Lévy flights can optimize search efficiencies. The hypothesis stems from a rigorous theory of one-dimensional searching and from simulation data for two-dimensional searching. The potential effectiveness of three-dimensional Lévy searches has not been examined but is central to a proper understanding of marine predators and T cells which have provided the most compelling empirical evidence for LW. Here I extend Lévy search theory from one to three dimensions. The new theory predicts that three-dimensional Lévy searching can be advantageous but only when targets are large compared with the perceptual range of the searchers, i.e. only when foragers are effectively blind and need to come into contact with a target to establish its presence. This may explain why effective blindness is a common factor among three-dimensional Lévy walkers.

scholarly journals Survival probability of random walks and Lévy flights on a semi-infinite line

2017 ◽  
Vol 50 (46) ◽  
pp. 465002 ◽  
Author(s):  
Satya N Majumdar ◽  
Philippe Mounaix ◽  
Grégory Schehr
Keyword(s):  
Random Walks ◽  
Survival Probability ◽  
Lévy Flights ◽  
Levy Flights ◽  
Infinite Line

scholarly journals Multi-scaling properties of truncated Lévy flights

2000 ◽  
Vol 266 (4-6) ◽  
pp. 282-289 ◽  
Author(s):  
Hiroya Nakao
Keyword(s):  
Lévy Flights ◽  
Scaling Properties ◽  
Levy Flights
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