We prove a conjecture by Bertoin that the multidimensional elephant random walk (MERW) on the d-dimensional lattice is transient if d≥3. In dimensions d = 1, 2, we prove that phase transitions between recurrence and transience occur at p = (2d + 1)/(4d), which thus closes the question on the transience and recurrence of MERWs. Moreover, we provide a Berry-Esseen type bound for the elephant random walk if p≤3/4.
Shuo Qin is a Ph.D. student of Prof. Pierre Tarrès at NYU Shanghai. He received his bachelor's degree in Mathematics from Fudan University. His research is mainly about self-interacting random processes, especially random walks with reinforcement.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai