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Behaviour at Infinity and Harmonic Functions of Random Walks on Graphs

In: Probability Measures on Groups X

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  • Wolfgang Woess

    (Università di Milano, Dipartimento di Matematica)

Abstract

The purpose of this paper is to review results concerning the behaviour at inifinity of random walks on graphs and (as a special case) groups and closely related questions concerning the associated harmonic functions. The point of view adopted here is that of starting with an infinite graph (or some other combinatorial, geometric or algebraic structure) and then studying the interplay between properties of random walks on this object on one hand and the underlying structure itself on the other. Thus, a random walk is a time-homogeneous Markov chain whose transition probabilities are adapted in some way (which has to be specified more precisely) to the given graph structure.

Suggested Citation

  • Wolfgang Woess, 1991. "Behaviour at Infinity and Harmonic Functions of Random Walks on Graphs," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 437-458, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_33
    DOI: 10.1007/978-1-4899-2364-6_33
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