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Step-reinforced random walks and one-half

Published 26 Feb 2024 in math.PR | (2402.16396v2)

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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