2021/01/18 by Sam Mellick, Mellick, Sam
Computer Science · Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #Random Matrices and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2101.07238
openalex publication_date 2021/01/18 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We define a probability measure preserving and r-discrete groupoid that is associated to every invariant point process on a locally compact and second countable group. This groupoid governs certain factor processes of the point process, in particular the existence of Cayley factor graphs. With this method we are able to show that point processes on amenable groups admit all (and only admit) Cayley factor graphs of amenable groups, and that the Poisson point process on groups with Kazhdan's Property (T) admits no Cayley factor graphs. This gives examples of pmp countable Borel equivalence relations that cannot be generated by any free action of a countable group.