%0 Journal Article
%T Dirichlet forms and stochastic completeness of graphs and subgraphs
%A Matthias Keller
%A Daniel Lenz
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0904.2985v2