Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
- Resource Type
- Working Paper
- Authors
- Wojciechowski, Radosław K.
- Source
- Subject
- Mathematics - Metric Geometry
Mathematical Physics
Mathematics - Probability
Primary 39A12, Secondary 05C63, 58J35
- Language
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.