Step-reinforced random walks and one-half

Shuo Qin

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arXiv · 2402.16396

Step-reinforced random walks and one-half

Shuo Qin

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Abstract

Under suitable moment assumptions, we show that a genuinely d-dimensional step-reinforced random walk undergoes a phase transition between recurrence and transience in dimensions $d=1,2$, and that it is transient for all reinforcement parameters in dimensions $d\geq 3$, which solves a conjecture of Bertoin.

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Shuo Qin. 2024-02-26. Step-reinforced random walks and one-half. https://arxiv.org/abs/2402.16396

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