Volume growth, spectrum and stochastic completeness of infinite graphs

By Matthias Keller, Daniel Lenz, Radoslaw K. Wojciechowski. 2011

80 citations recorded by the source corpus.

We study the connections between volume growth, spectral properties and stochastic completeness of locally finite weighted graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic incompleteness and discreteness of the spectrum. We then use these graphs to give some comparison results for both stochastic completeness and estimates on the bottom of the spectrum for general locally finite weighted graphs.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1d38cdb8fc0f8526eab725342642229fcee94fd0

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Cheeger inequalities for unbounded graph Laplacians (2012, background): “Lower bounds by curvature In this section we give a lower bound on the isoperimetric constant by a quantity that is sometimes interpreted as a curvature [11, 29, 39].”
Some constructions for the fractional Laplacian on noncompact manifolds (2012, background): “Note that heat kernel estimates are also valid for the Laplacian on graphs, see for instance the recent studies [28], [48] and references therein as [66].”
Volume growth and stochastic completeness of graphs (2012, background): “Necessary and suﬃcient criteria for stochastic completeness of weakly symmetric graphs are established in [22].”