Random Trees

Summary

The study of randomly generated trees is a growing field with connections to stochastic processes, combinatorics, and computer science. This course provides an introduction to the field aimed at advanced students. Topics include asymptotic properties and limits of conditioned Galton-Watson trees and related models. We will also discuss methods for the simulation and visualization of random trees.

Time and place

Due to the coronavirus pandemic the course will be held online using TUWEL. All announcements and lecture materials (zoom meeting data, videos, lecture notes, exercise sheets, homework solutions) will be posted on this platform.

Exam regulations

Gebundenes Wahlfach in Ausgewählte Themen der Wahrscheinlichkeitstheorie

Literature

• Aldous, David. The continuum random tree. I.Ann. Probab., 19(1):1–28, 1991
• Aldous, David. The continuum random tree. II. An overview. In Stochastic analysis, volume 167 of London Math. Soc. Lecture Note Ser., pages 23–70. Cambridge Univ. Press, 1991.
• Aldous, David. The continuum random tree. III. Ann. Probab., 21(1):248–289, 1993.
• Drmota, Michael. Random trees. An interplay between combinatorics and probability. SpringerWienNewYork, Vienna, 2009. xviii+458 pp.
• Janson, Svante. Simply generated trees, conditioned Galton-Watson trees, random allocations and condensation. Probab. Surv., 9:103–252, 2012.

Introduction video