Titlebook: Random Walks on Infinite Groups; Steven P. Lalley Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusive license t

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Markov Chains and Harmonic Functions,natural setting for the theory is the world of countable-state .. Random walks on finitely generated groups are Markov chains; as we will see, so are a number of auxiliary processes constructed from random walks.

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Martingales,tions in . is isomorphic to the space of real-valued functions on the boundary .. Is there an analogous characterization of the space of harmonic functions on the entire state space? The answer, as we will show in Chapter ., is tied up with the limiting behavior of harmonic functions along Markov chain paths.

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archers.Includes supplementary material: .The Encyclopedia of Mathematics Education is a comprehensive reference text, covering every topic in the field with entries ranging from short descriptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theorie

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Steven Lalleyptions to much longer pieces where the topic warrants more elaboration. The entries provide access to theories and to research in the area and refer to the leading publications for further reading. The Encyclopedia is aimed at graduate students, researchers, curriculum developers, policy makers, and

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