Subdiagrams of Bratteli diagrams and measure convergence

Assistant Professor Sergii Bezuglyi

The main focus of this talk is on subdiagrams of generalized Bratteli diagrams and the problem of extending tail invariant probability measures from subdiagrams to the ambient diagram. We establish necessary and sufficient conditions for the finiteness of such extensions, formulated in terms of incidence matrices. Several classes of generalized Bratteli diagrams and their subdiagrams are analyzed in detail, including simple, stationary, and bounded-size diagrams. We give explicit examples of generalized Bratteli diagrams that admit no tail invariant probability measures, a phenomenon absent for standard Bratteli diagrams with finite vertex sets. Finally, we address convergence questions for sequences of invariant measures arising from approximations by subdiagrams, clarifying the relationship between combinatorial structure and measure-theoretic behavior.

The talk is based on a joint paper with P. Jorgensen, O. Karpel, T. Raszeja, and S. Sanadhya.

To participate in this event virtually via Zoom, go to https://uiowa.zoom.us/j/95316149275.