Asymptotics for the Expected Maximum of Random Walks and Lévy Flights with a Constant Drift

Philippe Mounaix, Satya N. Majumdar, Gregory Schehr

In this paper, we study the large $n$ asymptotics of the expected maximum of an $n$-step random walk/Lévy flight (characterized by a Lévy index $1<\mu \le 2$) on a line, in the prese…