Branching random walk with innite progeny mean
In this talk we discuss the extremes of branching random walks under the assumption that the underlying Galton-Watson tree has in nite progeny mean. It is assumed that the displacements are either regularly varying or they have lighter tails. In the regularly varying case, it is shown that the point process sequence of normalized extremes converges to a Poisson random measure. In the lighter-tailed case, we study the asymptotics of the scaled position of the rightmost particle in the n-th generation and show the existence of a non-trivial constant. This is a joint work with Souvik Ray (Stanford), Parthanil Roy (ISI, Bangalore) and Philippe Soulier (Universite Paris Nanterre).