Senile reinforced random walks

M. Holmes, A. Sakai

Research output: Contribution to journalArticlepeer-review

9 Citations (SciVal)


We consider random walks with transition probabilities depending on the number of consecutive traversals nn 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)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.
Original languageEnglish
Pages (from-to)1519-1539
Number of pages1
JournalStochastic Processes and their Applications
Issue number10
Publication statusPublished - Oct 2007


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