February 26, 2024Open Access

Recurrence and transience of step-reinforced random walks

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Resumen

We solve a conjecture raised by Bertoin (personal communication) on the step-reinforced random walk, a non-Markovian process generalizing the elephant random walk. We show that, under a 2+-th moment condition, it undergoes a phase transition in dimensions d=1, 2 between recurrence and transience, and that it is transient for all parameters in dimension d 3.

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Shuo Qin (Mon,) studied this question.

synapsesocial.com/papers/68e779e4b6db6435876ee84c https://doi.org/https://doi.org/10.48550/arxiv.2402.16396

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