Perpetual cutoff method and discrete Ricci curvature bounds with exceptions

Abstract

One of the main obstacles regarding Barky Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds on parts of the graph. Moreover, we sharply upper bound the distance to the exception set for graphs having uniformly positive Bakry-Emery curvature everywhere but on the exception set.

References in corpus (5)

• Entropic Ricci curvature bounds for discrete interacting systems
• Bakry-Emery curvature and diameter bounds on graphs
• Bakry-Émery curvature functions of graphs
• A discrete log-Sobolev inequality under a Bakry-Emery type condition
• Distance bounds for graphs with some negative Bakry-Émery curvature