On minimal topological models for non-invariant measured actions

In 1989, Benjamin Weiss proved that for a countable group G, there exists a global minimal G-flow which is a topological model for every essentially free p.m.p. Borel G-action. In this talk, I will present our vast generalization, asserting that any essentially free Borel measured action (without the p.m.p. assumption), admits a minimal compact model. Moreover, we show that given a random walk on the group, there exists a global minimal topological model for all essentially free stationary Borel actions.

Based on joint work with Yair Hartman.