LFU:online

Absolvents should acquire the abilities to understand and express the contents of the course. In particular, the students should be familiar with topics in the context of Markov chains and random walks on finite and infinite graphs and problems such as: recurrence and transience, stationary distribution, limit laws for random walks, mixing times.

In this course we will investigate Markov chains (discrete random processes) on finite and infinite graphs and groups and we would like to understand their long time behaviour: recurrence and transience, limit laws (central limit theorems, law of iterated logarithms, convergence results), stationary distributions, cover times, mixing times. We will eventually analyse random graphs and random trees, branching processes, and connection between random walks and electrical networks.

Continuous assessment (based on regular written and/or oral contribution by participants).

Assessment is based on the evaluation of homework, presentations given by students in the exercise classes and a written exam.

Ariel Yadin: "Harmonic functions and random walks on groups", 2024, Cambridge University Press.

Wolfgang Woess: "Denumerable Markov chains".

Rick Durett: "Probability: Theory and Examples"

Russell Lyons and Yuval Peres: "Probability on trees and networks"

Gregory F. Lawler and Vlada Limic: "Random walk: a modern introduction"

Geoffrey R. Grimmett and David R. Stirzaker: "Probability and random processes"

Stochastics 1 and 2. Introduction to higher Stochastics is not necessarily needed.

Basic knowledge of stochastic processes is required.

The course will be given in English.