Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

Abstract

In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.

13 pages, Added a section with examples

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Cited by in corpus (3)

• Li-Yau inequality under $CD(0,n)$ on graphs
• Liouville property and non-negative Ollivier curvature on graphs
• Every Salami has two ends