Recurrence and transience of step-reinforced random walks
Recurrence and transience of step-reinforced random walks
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+$\delta$-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 …