Probability measures on topological groups and related problems in harmonic and functional analysis

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Probability Measures on Topological Groups and Related Problems in Harmonic and Functional Analysis The main topic of this research concerns certain aspects of the asymptotic (i.e., large time) behaviour of random walks on groups. Although the theory of random walks has, generally speaking, a strongly applied flavour, this research has to do mainly with the foundations of the theory and its connections to other fields of mathematics. The theory of probability measures and random walks on groups interacts in a nontrivial and deep way with several fields of mathematics. In addition to purely probabilistic methods, mathematical tools of harmonic and functional analysis, ergodic theory, and the theory of topological groups have to be involved to make progress. This interaction very often leads to nontrivial problems and solutions which can be of considerable interest not only within but also outside the theory of probability.