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Resistance Boundaries of Infinite Networks
[chapter]

2011
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Random Walks, Boundaries and Spectra
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We study the boundary theory of a connected weighted graph G from the viewpoint of stochastic integration. For the Hilbert space HE of Dirichlet-finite functions on G, we construct a Gel'fand triple S ⊆ HE ⊆ S . This yields a probability measure P on S and an isometric embedding of HE into L 2 (S , P), and hence gives a concrete representation of the boundary as a certain class of "distributions" in S . In a previous paper, we proved a discrete Gauss-Green identity for infinite networks which

doi:10.1007/978-3-0346-0244-0_7
fatcat:fmv7g6nh3vebdghgctgeswip6a