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On completion of this couse, students have acquired a deep knowledge of methods used in the theory of random walks. Moreover they are familiar with relevant mathematical literature and can judge its mathematical content. They are able to examine problems related to random walks and matrices in a creative and methodically correct manner and to present the result of those examinations in written form and orally as to be understood well by experts.

This research seminar offers the opportunity to present one's own research results, or explore and present a current topic from the theory of random walks and probability on trees and networks. We will concentrate on several research articles on random walks and other active research areas in stochastics.

Disscussions and presentations of recent research papers in random walks.

Continuous assessment (based on regular written and oral contributions by the participants).

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"