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2021S, UE, 1.0h, 1.5EC

## Merkmale

• Semesterwochenstunden: 1.0
• ECTS: 1.5
• Typ: UE Übung
• Format der Abhaltung: Distance Learning

## Lernergebnisse

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

## Inhalt der Lehrveranstaltung

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.

## Methoden

Probabilistic and combinatorial methods

Mündlich

## Leistungsnachweis

Presenting homework solutions

## LVA-Anmeldung

Von Bis Abmeldung bis
18.02.2021 00:00 30.06.2021 00:00 30.06.2021 00:00

## Curricula

StudienkennzahlSemesterAnm.Bed.Info
860 GW Gebundene Wahlfächer - Technische Mathematik

## Literatur

Es wird kein Skriptum zur Lehrveranstaltung angeboten.

## Vorkenntnisse

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

## Sprache

bei Bedarf in Englisch