On the uniqueness class, stochastic completeness and volume growth for graphs
Xueping Huang, Matthias Keller, Marcel Schmidt
Abstract
In this note we prove an optimal volume growth condition for stochastic completeness of graphs under very mild assumptions. This is realized by proving a uniqueness class criterion for the heat equation which is an analogue to a corresponding result of Grigorâyan on manifolds. This uniqueness class criterion is shown to hold for graphs that we call globally local, i.e., graphs where we control the jump size far outside. The transfer from general graphs to globally local graphs is then carried out via so-called refinements.
Topics & Concepts
UniquenessMathematicsCompleteness (order theory)Class (philosophy)JumpDiscrete mathematicsCombinatoricsMathematical analysisPhysicsArtificial intelligenceComputer scienceQuantum mechanicsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsMarkov Chains and Monte Carlo Methods