Self-interacting random walks

Details Self-interacting random walks Self-interacting random walks

2012-03-15

arxiv.org/abs/1203.3459v1

Mathematics

Probability

Scientific paper

Let $\mu_1,... \mu_k$ be $d$-dimensional probability measures in $\R^d$ with mean 0. At each step we choose one of the measures based on the history of the process and take a step according to that measure. We give conditions for transience of such processes and also construct examples of recurrent processes of this type. In particular, in dimension 3 we give the complete picture: every walk generated by two measures is transient and there exists a recurrent walk generated by three measures.

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