Dirichlet forms and stochastic completeness of graphs and subgraphs

Details Dirichlet forms and stochastic completeness of graphs and subgraphs Dirichlet forms and stochastic completeness of graphs and subgraphs

2009-04-20

arxiv.org/abs/0904.2985v2

Mathematics

Functional Analysis

27 pages

Scientific paper

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 $\ell^p$, $1\leq p < \infty$, 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.

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