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

Research output: Contribution to journalReview articlepeer-review

189 Scopus citations


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 languageEnglish
Pages (from-to)1-12
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - 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.


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