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Abstract
We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient geometric condition for essential selfadjointness and explicitly determine the generators of the associated semigroups on all ℓp, 1 ≦ p < ∞, in this case. We characterize stochastic completeness thereby generalizing all earlier corresponding results for graph Laplacians. Finally, we study how stochastic completeness of a subgraph is related to stochastic completeness of the whole graph.
Received: 2010-03-18
Revised: 2010-12-12
Published Online: 2011-07-24
Published in Print: 2012-05
©[2012] by Walter de Gruyter Berlin Boston
