Abstract
Let µ1,...,µ k 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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Peres, Y., Popov, S. & Sousi, P. On recurrence and transience of self-interacting random walks. Bull Braz Math Soc, New Series 44, 841–867 (2013). https://doi.org/10.1007/s00574-013-0036-4
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DOI: https://doi.org/10.1007/s00574-013-0036-4