Nicolò Paviato

Central Limit Theorems for Finitary Factors of iid Processes

Given a multidimensional -subshift with an invariant probability measure, we are interested in statistical limit theorems of the Birkhoff sums of regular observables. Although the literature in d = 1 is quite comprehensive, for multi-parameter actions the theory is much less developed. In this talk we present our techniques to study such systems, under the assumption that the system is a finitary factor of a iid process with suitable coding radius estimates. We prove a central limit theorem with rates and convergence to a Brownian sheet. Our results can be applied to classical models in
statistical mechanics, such as the Ising model, the Potts model, proper colourings, the hard-core model, the Widom–Rowlinson model and the beach model. This is joint work with Zemer Kosloff and Raimundo Briceno.