Statistical physics of 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

23 Scopus citations

Abstract

We apply the theory of random walks to quantitatively describe the general problem of how to search efficiently for randomly located objects that can only be detected in the limited vicinity of a searcher who typically has a finite degree of "free will" to move and search at will. We illustrate Levy flight search processes by comparison to Brownian random walks and discuss experimental observations of Lévy flights in the special case of biological organisms that search for food sites. We review recent findings indicating that, an inverse square probability density distribution P(ℓ) ∼ ℓ-2 of step lengths ℓ can lead to optimal searches. Finally we survey the explanations put forth to account for these surprising findings.

Original languageEnglish
Pages (from-to)102-108
Number of pages7
JournalBrazilian Journal of Physics
Volume31
Issue number1
DOIs
StatePublished - Mar 2001

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