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arXiv · 2310.14927

Neumann semigroup, subgraph convergence, form uniqueness, stochastic completeness and the Feller property

Matthias Keller·Florentin Münch·Radosław K. Wojciechowski
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Abstract

We study heat kernel convergence of induced subgraphs with Neumann boundary conditions. We first establish convergence of the resulting semigroups to the Neumann semigroup in $\ell^2$. While convergence to the Neumann semigroup always holds, convergence to the Dirichlet semigroup in $\ell^2$ turns out to be equivalent to the coincidence of the Dirichlet and Neumann semigroups while convergence in $\ell^1$ is equivalent to stochastic completeness. We then investigate the Feller property for the Neumann semigroup via generalized solutions and give applications to graphs satisfying a condition on the edges as well as birth-death chains.

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Matthias Keller, Florentin Münch, Radosław K. Wojciechowski. 2023-10-23. Neumann semigroup, subgraph convergence, form uniqueness, stochastic completeness and the Feller property. https://arxiv.org/abs/2310.14927

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