DSNT Seminar: Thermodynamic formalisms for Markov subshifts on 𝑑-trees

Abstract: The talk is based on a joint with Jung-Chao Ban and Guan-Yu Lai, which investigates the thermodynamic formalism for Markov subshifts on 𝑑-trees under the irreducible assumption. The study is motivated by the work by Burton-Pfister-Steif, in which they discovered that the variational principle "fails" for such systems on 𝑑-trees even for full-shifts. In our work, we extend their discovery to subshifts with merely irreducible assumption, and, in particular, prove a version of law of large numbers for irreducible Markov chains on 𝑑-trees, which is a slight improvement for existing results in the literature.

This is a seminar in our seminar series on Dynamical Systems and Number Theory (DSNT).