A nonlinear characterization of stochastic completeness of graphs

Marcel Schmidt and Ian Zimmermann

Mathematische Nachrichten, 2025, vol. 298, issue 3, 925-943

Abstract: We study nonlinear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semilinear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a nonlinear setting. We provide characterizations for this property in terms of a semilinear Liouville theorem. It is employed to establish a nonlinear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.

Date: 2025
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