Stochastic adding machines based on Bratteli diagrams

Danilo Antonio Caprio, Ali Messaoudi, Glauco Valle

Published 2017-12-27Version 1

In this paper, we define some Markov Chains associated to Vershik maps on Bratteli diagrams. We study probabilistic and spectral properties of their transition operators and we prove that the spectra of these operators are connected to Julia sets in higher dimensions. We also study topological properties of these spectra.