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Step-reinforced random walks and one-half

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arxiv 2402.16396 v2 pith:3JX4RDFD submitted 2024-02-26 math.PR

Shuo Qin This is my paper · ORCID
classification math.PR
keywords dimensionsrandomstep-reinforcedassumptionsbertoinconjectured-dimensionalgenuinely
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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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