Abstract

We consider a supercritical branching random walk on the real line in the so called kappa-case, where the additive martingale and derivative martingale both converge a.s. and in L^p (p>1) to some non-degenerate random variables. We study the tail behaviors of these martingale limits. We also discuss how this is related to the large deviation probabilities of the size of level sets. This is based on joint works with Xinxin Chen (BNU) and Loïc de Raphélis (Orléans)