Harmonic Functions on Bratteli Diagrams

Puja Solaiappan

Abstract: Bratteli diagrams are graded graphs used to model transformations acting on Cantor and standard Borel spaces. Their combinatorial structure allows one to study dynamical properties of transformations transparently. On the other hand, the path space of a Bratteli diagram can be considered as a Markov process with transition probabilities determined by the incidence matrices. In the talk, we consider the space-time harmonic functions for some classes of reducible Bratteli diagrams and transient Markov processes. We present explicit formulas for harmonic functions and the Green's function for Bratteli diagrams (and their sub diagrams) with triangular incidence matrices in discrete and measurable settings. We also discuss minimal harmonic functions on these diagrams and other related results. The talk is based on a joint work with Sergii Bezuglyi and Olena Karpel.

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