Stochastic adding machines based on Bratteli diagrams - Caprio, Danilo A. [UNESP]; Messaoudi, Ali [UNESP]; Valle, Glauco (Cellule MathDoc/Centre Mersenne, 2020)
In this paper, we define some Markov chains associated with 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.
Keywords: Bratteli diagrams; Fibered Julia sets; Markov chains; Spectrum of transition operators; Stochastic Vershik map