Coalescence in branching processes
Department of Statistics
Iowa State University
Johnson Center G19 - Gold Room
4400 University Drive, Fairfax, VA 22030
Time: 11:00 A.M. - 12:00 P.M.
Date: Friday, Sep 14, 2012
Consider a branching tree. Go to the nth generation. If there are at least two vertices in that generation pick two of them at random by srswor (simple random sampling without replacement) and trace their lines of descent back in time till they meet. Call that generaion Xn. Do the same thing with all individuals in the nth generation. Call that Yn. In this talk we discuss the distributions of Xn and Yn and their asymptotics for Galton Watson trees as n goes to infinity for single and multitype cases for the four cases: subcritical, critical, supercritical, explosive.Applications to branching random walks will also be discussed.