Probability Theory on Trees and Networks

WS 2020/21

General

Lecture:

Monday, 4 pm - 6 pm, 
Wednesday, 2 pm - 4 pm, 

Lecturer: 

Jun.-Prof. Chiranjib Mukherjee

Assistance: 

Yannic Bröker

KommVV:

Eintrag der Vorlesung im kommentierten Vorlesungsverzeichnis
Eintrag der Übungen im kommentierten Vorlesungsverzeichnis

Course syllabus:

The course is concerned with behavior of random walks on certain infinite graphs which are currently in vigorous development. This is a topic of dicrete probability are full of surprising and beautiful results which lie at the crossroads of probability theory, other areas of mathematics (e.g. geometry) and theoretical  computer science.  There are three major types of graphs which we will be studying: trees, Cayley graphs of groups and planar graphs. 

Our major topics include random walks and their intimate connection to electrical networks; uniform spanning trees, their limiting forests, and their marvelous relationships with random walks and electrical networks; branching processes; percolation and the powerful, elegant
mass-transport technique; isoperimetric inequalities and how they relate to both random walks and percolation. Connections among these topics are pervasive and rich, making for surprising and enjoyable proofs.

Learnweb:

Please enrol in the Learnweb with the password PTOTAN202021.

Course assessment:

Succesfully completing 50% of the exercise sheets as well as an oral/ written exam at the end of the course.

Tutorial

Tutorial:

Monday, 2 pm - 4 pm

Problem sets:

Exercise Sheet 1 Exercise Sheet 2 Exercise Sheet 3 Exercise Sheet 4