Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage...
After successful completion of the course, students are able to...
- differentiate types of combinatorial trees, such as plane trees, unordered trees, labelled trees, ...
- use the Aldous-Broder algorithm to generate uniform spanning trees
- describe the asymptotic growth of a supercritical Galton-Watson process via the Kesten-Stigum theorem
- prove local weak convergence of simply generated trees towards Kesten's modified Galton-Watson tree
- prove Gromov-Hausdorff convergence of simply generated trees towards Aldous' Brownian continuum random tree
- simulate and visualize random trees using Python
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.
