Ends of stationary metric measure spaces
classification
🧮 math.DS
math.GNmath.PR
keywords
stationaryendsmanifoldsmeasuremetricrandomspacesanalogy
read the original abstract
We prove that stationary random metric measure spaces have 0,1,2 or a Cantor space of ends. This notion includes stationary random graphs, manifolds and discrete subgroups. In the case of surfaces, we classify all possible homeomorphism types, in analogy with the work of Biringer and Raimbault on unimodular Riemannian manifolds. Our approach relies on a general "no geometric core" principle and an analysis of finite versus infinite expected return times.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.