Recorded 29 August 2022. Matteo Tanzi of New York University presents "Self-consistent transfer operators for high-dimensional expanding coupled maps" at IPAM's Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond. Abstract: Recently, much progress has been made in the mathematical study of self-consistent transfer operators describing the thermodynamic limit of globally coupled expanding maps. Existence of equilibrium measures (fixed points for the self-consistent transfer operator) has been established together with their stability under perturbations and linear response. 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 will quantify this relation in the case where the coupled dynamics is uniformly expanding and I will compare the statistical behavior of the (finite dimensional) coupled system and the fixed point of the self-consistent operator. 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 will quantify this relation and show that, under suitable assumptions, an equilibrium state of the thermodynamic limit, although it can be far from any invariant measure of the finite system, it is “almost “ invariant and describes its statistical behavior for extremely long transients whose duration scales exponentially with the number of coupled units. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/reconstructing-network-dynamics-from-data-applications-to-neuroscience-and-beyond/?tab=overview