Li-Yau inequality for unbounded Laplacian on graphs

Abstract

In this paper, we derive Li-Yau inequality for unbounded Laplacian on complete weighted graphs with the assumption of the curvature-dimension inequality $CD{E}^{\prime }(n,K)$, which can be regarded as a notion of curvature on graphs. Furthermore, we obtain some applications of Li-Yau inequality, including Harnack inequality, heat kernel bounds and Cheng's eigenvalue estimate. These are first kind of results on this direction for unbounded Laplacian on graphs.

19 pages

References in corpus (1)

• Remarks on curvature dimension conditions on graphs

Cited by in corpus (3)

• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
• Li-Yau inequality under $CD(0,n)$ on graphs
• Ancient caloric functions on graphs with unbounded Laplacians