Details

Beamer presentation of the course delivered during the first lecture (28 Mb).

Lecture 1 -

Addendum to Lecture 1

- Exercise given at the end of Lecture 1

- Its solution

Lecture 2 -

Exercise given at the end of Lecture 2

- Its solution

Lecture 3

- Exercise given at the end of Lecture 3

- Its solution

Lecture 4

- Exercise given at the end of Lecture 4

- Its solution

Lecture 5

- Exercise given at the end of Lecture 5

- Its solution

Lecture 6

Lecture 7

- Exercise given at the end of Lecture 7

- Its solution

Lecture 8

- Exercise given at the end of Lecture 8

- Its solution

Lecture 9

- Exercise given at the end of Lecture 9

- Its solution

Lecture 10

Lecture 11

Lecture 12

This course will focus on geometric aspects of random discrete and continuous random trees. We will use various tools from combinatorics and probability which may be useful in other contexts. Depending on the audience, we will cover some of the following topics:

1. Galton-Watson trees, and their coding by random walks
2. Combinatorial tools for enumerating trees
3. Local limits of Galton-Watson trees
4. Scaling limits of Galton-Watson trees:
       a) Introduction to the Gromov-Hausdorff topology, which is a topology on classes of compact metric spaces and which gives a precise setting for studying convergence of discrete trees towards continuous trees.
       b) Convergence of large rescaled discrete Galton-Watson trees towards the Brownian Random Tree, which is a random continuous tree coded by Brownian motion.
5. Local times of Brownian motion and Itô's excursion theory in the study of random trees.

We shall only assume prior knowledge of the basics of measure-theoretic probability theory.

Prüfung

Prüfung

Modul: 06.02.2015 9:00-12:00, Raum: Y27H12 Plätze: 50, Typ: mündlich