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Senile reinforced random walks


Reference:

Holmes, M. and Sakai, A., 2007. Senile reinforced random walks. Stochastic Processes and their Applications, 117 (10), pp. 1519-1539.

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Abstract

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.

Details

Item Type Articles
CreatorsHolmes, M.and Sakai, A.
DOI10.1016/j.spa.2007.02.003
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code6974

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