Description
Harmonic Functions and Random Walks on Groups presents a comprehensive study of the interplay between harmonic analysis and probability theory on groups. This advanced text examines how random walks on group structures generate harmonic functions and investigates the fundamental properties that arise from this relationship.
The book covers key topics including the theory of random walks on countable groups, harmonic functions in the context of group actions, and the probabilistic methods used to analyze their behavior. Special attention is given to amenable groups, growth conditions, and the classification of harmonic functions with specific growth rates.
Written for graduate students and researchers in mathematics, this volume provides rigorous proofs and explores applications to geometric group theory and functional analysis. The treatment combines classical results with modern developments in the field.
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