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

Abstract

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.

5 pages, 4 figures

References in corpus (5)

• Understanding individual human mobility patterns
• The scaling laws of human travel
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
• Amnestically induced persistence in random walks

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