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Harmonic functions on infinite graphs

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Su un grafo infinito, localmente finito si considera un «Laplaciano» dato da una matrice stocastica di transizione legata alla struttura del grafo. Si descrive il collegamento fra il cono delle funzioni armoniche positive e lo spazio degli «ends» del grafo. Si presentano i risultati noti per vari classi di grafi, in particolare per grafi di Cayley di gruppi infiniti.

Summary

On an infinite, locally finite graph, a «Laplacian» is considered which is given by a stochastic transition matrix linked with the graph structure. We describe the interplay between the cone of positive harmonic functions and the space of ends of the graph. We give a survey of known results for several classes of graphs, in particular for Cayley graphs of infinite groups.

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Author notes

  1. Wolfgang Woess

    Present address: Dipartimento di Matematica «F. Enriques», Università di Milano, Via C. Saldini, 50-20133, Milano, Italia

Authors and Affiliations

  1. Institut fur Mathematik und Angewandte Geometrie Montanuniversität, A-8700, Leoben, Austria

    Wolfgang Woess

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  1. Wolfgang Woess
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(Conferenza tenuta il 16 aprile 1986)

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Woess, W. Harmonic functions on infinite graphs. Seminario Mat. e. Fis. di Milano 56, 51–63 (1986). https://doi.org/10.1007/BF02925134

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