Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
The goal of this article is to survey various results concerning stochastic completeness of graphs. In particular, we present a variety of formulations of stochastic completeness and discuss how a discrepancy between uniqueness class and volume growth criteria in the continuous and discrete settings...
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | The goal of this article is to survey various results concerning stochastic
completeness of graphs. In particular, we present a variety of formulations of
stochastic completeness and discuss how a discrepancy between uniqueness class
and volume growth criteria in the continuous and discrete settings was
ultimately resolved via the use of intrinsic metrics. Along the way, we discuss
some equivalent notions of boundedness in the sense of geometry and of
analysis. We also discuss various curvature criteria for stochastic
completeness and discuss how weakly spherically symmetric graphs establish the
sharpness of results. |
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DOI: | 10.48550/arxiv.2010.02009 |