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arXiv · 1109.3137

After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs

Robert Carlson
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Abstract

Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Compactness and a novel connectivity hypothesis for the completed graphs play an essential role. A version of the Dirichlet problem is solved. Self adjoint Laplace operators and the probability semigroups they generate are constructed using reflecting and absorbing conditions on subsets of the graph boundary.

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Robert Carlson. 2011-09-14. After the Explosion: Dirichlet Forms and Boundary Problems for Infinite Graphs. https://arxiv.org/abs/1109.3137

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