Title: Thermodynamic Formalism Out of Equilibrium
Abstract: We introduce the notion of TDFOE studying the thermodynamic formalism on topological Markov shifts where the potential is random, depending on a Gibbs random walk on a compact metric space. We introduce the associated Pressure Out of Equilibrium, and discuss its properties (e.g. variational principle, linear response), and applications (Azuma inequality for potentials expanding on average w.r.t. to a Gibbs measure). We discuss the associated {\em semi-Ruelle operator} which generates the POE, and its properties (e.g. existence of conformal measures, spectral radius). We provide an application by studying Effectively Co-Expanding on Average diffeomorphisms on closed manifolds (this is a $C^1$-open condition). We prove quasi-compactness (and later a spectral gap) for the Averaged Semi-Ruelle operator on a Sobolev space. Notably, the diffeos are allowed to be highly dissipative. Finally, we mention a few applications such as: Dimension bounds on the stationary measure, and effective CLT and LLT for the (not necessarily invariant) volume measure.
This talk is based on three works, one joint with Aaron Brown and Federico Rodriguez-Hertz, and one joint with Yeor Hafouta.
Bryna Kra
(847) 491-5567
Email