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Recurrence and Transience of Multidimensional Elephant Random Walks

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SSD - Stochastic systems for anomalous diffusion

We prove a conjecture by Bertoin that the multidimensional elephant random walk on Z^d is transient in dimensions d ≥ 3. We show that it undergoes a phase transition in dimensions d = 1, 2 between recurrence and transience at p = (2d + 1)/(4d). We also generalize these results to the step-reinforced random walk under mild moments conditions.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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