Coalescence in Branching Trees and Branching Random Walks

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 Xn. In this talk we discuss the behavior of the distribution of Xn 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.

Series:
Microsoft Research Talks
Date:
Speakers:
Krishna B. Athreya
Affiliation:
Iowa State University

    • Portrait of Jeff Running

      Jeff Running

Series: Microsoft Research Talks