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}
}
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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