Step-reinforced random walks and one-half

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 $d\ge 3$, which solves a conjecture of Bertoin.

38 pages. This is the revised version of the previous paper Recurrence and Transience of Step-Reinforced Random Walks