Levy flights in random searches

G. M. Viswanathan; V. Afanasyev; Sergey V. Buldyrev; Shlomo Havlin; M. G.E. Da Luz; E. P. Raposo; H. Eugene Stanley

doi:10.1016/S0378-4371(00)00071-6

Levy flights in random searches

G. M. Viswanathan, V. Afanasyev, Sergey V. Buldyrev, Shlomo Havlin, M. G.E. Da Luz, E. P. Raposo, H. Eugene Stanley

Department of Physics

Research output: Contribution to journal › Review article › peer-review

208 Scopus citations

Abstract

We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate Levy flight foraging by comparison to Brownian random walks and discuss experimental observations of Levy flights in biological foraging. We review recent findings suggesting that an inverse square probability density distribution P(l) approx. l^-2 of step lengths l can lead to optimal searches. Finally, we survey the explanations put forth to account for these unexpected findings.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Physica A: Statistical Mechanics and its Applications
Volume	282
Issue number	1
DOIs	https://doi.org/10.1016/S0378-4371(00)00071-6
State	Published - 1 Jul 2000

Bibliographical note

Funding Information:
We thank N. Dokholyan, I.P. Fittipaldi, P.Ch. Ivanov, U. Laino, L.S. Lucena, M.L. Lyra, Roberto L. Santos, M.F. Shlesinger, B.D. Stosic and P. Trunfio for very useful discussions, and CNPq, NSF, and NIH for financial support.

Funding

We thank N. Dokholyan, I.P. Fittipaldi, P.Ch. Ivanov, U. Laino, L.S. Lucena, M.L. Lyra, Roberto L. Santos, M.F. Shlesinger, B.D. Stosic and P. Trunfio for very useful discussions, and CNPq, NSF, and NIH for financial support.

Funders	Funder number
National Science Foundation
National Institutes of Health
Conselho Nacional de Desenvolvimento Científico e Tecnológico

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10.1016/S0378-4371(00)00071-6

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abstract = "We review the general search problem of how to find randomly located objects that can only be detected in the limited vicinity of a forager, and discuss its quantitative description using the theory of random walks. We illustrate Levy flight foraging by comparison to Brownian random walks and discuss experimental observations of Levy flights in biological foraging. We review recent findings suggesting that an inverse square probability density distribution P(l) approx. l-2 of step lengths l can lead to optimal searches. Finally, we survey the explanations put forth to account for these unexpected findings.",

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AU - Raposo, E. P.

AU - Stanley, H. Eugene

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Levy flights in random searches

Abstract

Bibliographical note

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