Random walks with preferential relocations to places visited in the past and their application to biology

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited s...

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Veröffentlicht in:Physical review letters 2014-06, Vol.112 (24), p.240601-240601, Article 240601
Hauptverfasser: Boyer, Denis, Solis-Salas, Citlali
Format: Artikel
Sprache:eng
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Zusammenfassung:Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.112.240601