We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. We show that if properties such as the Rokhlin property, topometric generics, and extreme amenability hold for the isometry group of the structure, then they also hold in the isometry group of the randomization.
"Isometry Groups of Borel Randomizations." Notre Dame J. Formal Logic 61 (2) 297 - 316, May 2020. https://doi.org/10.1215/00294527-2020-0008