Senile reinforced random walks

M. Holmes and A. Sakai

Stochastic Processes and their Applications, 2007, vol. 117, issue 10, 1519-1539

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.

Keywords: Random; walk; Reinforcement; Recurrence/transience; Diffusion; constant (search for similar items in EconPapers)
Date: 2007
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