Work

Infinite stationary measures of co‐compact group actions

Year: 2025

Type: article

Abstract: Let be a finitely generated group, and let be a nondegenerate, finitely supported probability measure on . We show that every co‐compact action on a locally compact Hausdorff space admits a nonzero ‐stationary Radon measure. The main ingredient of the proof is a stationary analog of Tarski's theorem: we show that for every nonempty subset there is a ‐stationary, finitely additive measure on that assigns unit mass to .

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70198

Authors: Mohammedsaid Alhalimi, Tom Hutchcroft, Minghao Pan, Omer Tamuz, Tianyi Zheng

Institutions: University of California, Berkeley, California Institute of Technology, University of California San Diego

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: Probability on Groups and Semigroups of Probabilities, Stationary random systems via an asymptotic approach, Percolation Theory and Related Topics