This week Kieran Power will be giving a talk entitled about “g-Measures in the Study of Random β-Transformations “. As usual we will be on Microsoft Teams at 4pm on the Friday.
Abstract: “We introduce the idea of β-expansions for non-integral β > 1, and then discuss the generating random β-transformation, which we can view as a suitable dynamical system. As an interlude we will then provide an exposition of the theory of g-measures most often associated with thermodynamical formalism, and illustrate some of their most useful properties and applications. Finally, inspired by the Dyson model coming from statistical physics, we explain how we use the machinery of g-measures to construct a new family of invariant measures for the random β-transformation for certain algebraic β.”