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arXiv · 2403.15125

A non-linear characterization of stochastic completeness of graphs

Marcel Schmidt·Ian Zimmermann
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Abstract

We study non-linear Schr\"odinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear setting. We provide characterizations for this property in terms of a semi-linear Liouville theorem. It is employed to establish a non-linear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.

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Marcel Schmidt, Ian Zimmermann. 2024-03-22. A non-linear characterization of stochastic completeness of graphs. https://arxiv.org/abs/2403.15125

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