Séminaire OrléansUniformly Expanding Coupled Maps: Self-Consistent Transfer Operators and Propagation of Chaos
Matteo Tanzi (LPSM, Paris)
Thursday 15 December 2022 14:00 - Orléans - Salle de Séminaires
Recently, much progress has been made in the mathematical study of self-consistent transfer operators which describe the thermodynamic limit of globally coupled maps. Conditions for the existence of equilibrium measures (fixed points for the self-consistent transfer operator) have been given and their stability under perturbations and linear response have been investigated. One of the main questions remaining open is to which extent the thermodynamic limit describes the evolution of the finite dimensional system.
In this talk, I am going to describe some novel developments answering this question for a system of N uniformly expanding coupled maps when N is finite but large. I will introduce self-consistent transfer operators that approximate the evolution of measures under the dynamics, and quantify this approximation explicitly with respect to N. Using this result, I will show that uniformly expanding coupled maps satisfy propagation of chaos when N tends to infinity, and I will characterize the absolutely continuous invariant measures for the finite dimensional system.