Coalescence in Branching Trees and Branching Random Walks

Опубликовано 22 июня 2016, 18:40

Consider a branching tree with one root at the origin. Assuming that at the n -th level there are at least two vertices. Pick two of them by simple random sampling without replacement. Now trace their lines back till they meet. Call that level X n . In this talk we discuss the behavior of the distribution of X n as n goes to infinity for the supercritical, critical, and subcritical Galton Watson branching trees. We also discuss the explosive case when the offspring mean is infinite and the offspring distribution is heavy tailed. We apply these results to study branching random walks. Some open problems will be described.