Codings of multitype trees and applications to branching processes I
主 题: Codings of multitype trees and applications to branching processes I
报告人: Professor Lo?c Chaumont (University of Angers, France)
时 间: 2014-06-13 8:30-9:30
地 点: 理科一号楼1418（概率论系列报告）
Lecture 1: The single type case. We first present the depth first search and the breadth first search algorithms of planar discrete trees. From this coding and the ballot theorem for downward skip free random walks, we derive the law of the total population of Bienaym\'e-Galton-Watson trees (BGW trees). Then we discuss some invariance principles. In particular, we show that BGW trees with square integrable progeny law conditioned by their total population, once properly renormalized, converge to a continuous tree which is coded by the Brownian normalized excursion.