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Reinforced Random Walks Under Memory Lapses

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Abstract

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability \(\theta \) and with probability \(1 - \theta \), the random walk performs a step independent of the past. We analyse its asymptotic behaviour, showing a law of large numbers and characterizing the diffusive and superdiffusive regions. We prove central limit theorems and law of iterated logarithm based on the martingale approach.

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Acknowledgements

The authors thank Christian Caamaño and Rodrigo Lambert for several comments. This work was partially supported by Fondecyt No. 11200500

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Authors and Affiliations

  1. Departamento de Estadística, Universidad del Bío-Bío. Avda. Collao 1202, CP, 4051381, Concepción, Chile

    Manuel González-Navarrete & Ranghely Hernández

Authors
  1. Manuel González-Navarrete
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  2. Ranghely Hernández
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Correspondence to Manuel González-Navarrete.

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Communicated by Irene Giardina.

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González-Navarrete, M., Hernández, R. Reinforced Random Walks Under Memory Lapses. J Stat Phys 185, 3 (2021). https://doi.org/10.1007/s10955-021-02826-x

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