Random Walks with Preferential Relocations to Places Visited in the Past and their Application to Biology

✍ Scribed by Boyer, Denis; Solis-Salas, Citlali

• Book ID: 127095257
• Publisher: The American Physical Society
• Year: 2014
• Tongue: English
• Weight: 476 KB
• Volume: 112
• Category: Article
• ISSN: 0031-9007
• DOI: 10.1103/physrevlett.112.240601

✦ Synopsis

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.