CSDC Seminar: Pressure at infinity and large deviations (Thomas Jordan)

We start by showing the connection between standard large deviation theory form probability and the topological pressure function from the thermodynamic formalism. We will illustrate with the case of coin tossing for large deviations and the doubling map for the thermodynamic formalism.  We will then show how this result can be adapted to the setting of symbolic dynamics with a countable alphabet. For this we will introduce the pressure at infinity and show how it connects to the rate function for large deviations. Joint work with Godofredo Iommi and Anibal Velozo.