104.589 AKWTH Random Trees
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2021S, UE, 1.0h, 1.5EC

Properties

  • Semester hours: 1.0
  • Credits: 1.5
  • Type: UE Exercise
  • Format: Distance Learning

Learning outcomes

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

Subject of course

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.

Teaching methods

  Probabilistic and combinatorial methods

Mode of examination

Oral

Lecturers

Institute

Examination modalities

Presenting homework solutions

 

Course registration

Begin End Deregistration end
18.02.2021 00:00 30.06.2021 00:00 30.06.2021 00:00

Curricula

Literature

No lecture notes are available.

Previous knowledge

Probability Theory: the basics of Markov chains, Martingales, and Brownian motion

Language

if required in English