Title: Asymptotic study of extremes in branching random walk
Authors: Ayan Bhattacharya - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: Discrete time branching random walk on real line is considered where the displacements have regularly varying tail. Due to heavy-dependence structure and non-stationarity among the positions of the particles in the $n$th generation, it is challenging to study the growth of extreme positions. We shall discuss asymptotics for the bulk behavior of $t$ extreme positions. As a consequence of heavy-dependence structure, a non-trivial strong cluster structure will appear in the limit.