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Senile reinforced random walks

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  • Holmes, M.
  • Sakai, A.

Abstract

We consider random walks with transition probabilities depending on the number of consecutive traversals n of the edge most recently traversed. Such walks may get stuck on a single edge, or have every vertex recurrent or every vertex transient, depending on the reinforcement function f(n) that characterizes the model. We prove recurrence/transience results when the walk does not get stuck on a single edge. We also show that the diffusion constant need not be monotone in the reinforcement.

Suggested Citation

  • Holmes, M. & Sakai, A., 2007. "Senile reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1519-1539, October.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:10:p:1519-1539
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    References listed on IDEAS

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    1. Roger Bidaux & Nino Boccara, 2000. "Correlated Random Walks With A Finite Memory Range," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 921-947.
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