Presentation av Examensarbete C i matematik: Recent development in conditioned Galton-Watson trees

  • Date:
  • Location: Polacksbacken 2215
  • Lecturer: Anton Falk
  • Contact person: Vera Koponen
  • Seminarium

Summary:

A Galton-Watson tree is a random tree, which was introduced as a mathematical model, to describe the evolution of family names. Such a tree is constructed by starting with a root and let this root have offspring according to some underlying offspring distribution. Then, each of these children gets offspring according to independent copies of the offspring distribution, and so on.

A conditioned Galton-Watson tree is a Galton-Watson tree conditioned on having n number of nodes. We investigate global and local limits of such trees, as n goes to infinity. We also investigate the distribution of the number of copies of a given tree in the limit, as well as the distribution of the number of nodes removed in an iterative leaf-cutting procedure.