Spatio-temporal large deviations principle for coupled circle maps. (Q1879866)

A large deviations principle (LDP) is established for the space-time empirical measure associated with certain dynamical systems, namely weakly coupled expanding circle maps on \(\mathbb{Z}^d\). To this end, the authors first construct a potential function \(\varphi\) defined on the state space \((S^1)^{\mathbb{Z}^d}\), and such that \((-\varphi)\) is playing the role of the logarithm of the Jacobian associated with the dynamics. This potential function appears naturally in a ``Volume lemma'' giving appropriate upper and lower bounds for the measure of all points whose orbit remains close to a fixed orbit; such bounds lie at the heart of the present work, and the announced LDP may then be established using thermodynamic formalism. Fortunately, many definitions and results concerning e.g. thermodynamic formalism are presented at the end of the article, which, altogether, is written with a very clear style.