# On recurrence and transience of self-interacting random walks

@article{Peres2013OnRA,
title={On recurrence and transience of self-interacting random walks},
author={Yuval Peres and Serguei Yu. Popov and Perla Sousi},
journal={Bulletin of the Brazilian Mathematical Society, New Series},
year={2013},
volume={44},
pages={841-867}
}
• Published 14 December 2013
• Mathematics
• Bulletin of the Brazilian Mathematical Society, New Series
Let µ1,...,µk be d-dimensional probabilitymeasures in ℝd with mean 0. At each time 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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