Furstenberg entropy spectra of stationary actions of semisimple Lie groups
Jérémie Brieussel, Tianyi Zheng · arXiv (Cornell University) · 2023
We determine Furstenberg entropy spectra of ergodic stationary actions of $SL(d,\mathbb{R})$ and its lattices. The constraints on entropy spectra are derived from a refinement of the Nevo-Zimmer projective factor theorem. The realisation part is achieved by means of building Poisson bundles over stationary random subgroups.