Self-Consistent Transfer Operators for High-Dimensional Expanding Coupled Maps

Explore the mathematical advancements in self-consistent transfer operators for high-dimensional expanding coupled maps in this 40-minute lecture by Matteo Tanzi from New York University. Delve into the recent progress made in studying the thermodynamic limit of globally coupled expanding maps, including the existence of equilibrium measures and their stability under perturbations. Examine the key question of how accurately the thermodynamic limit describes the evolution of finite-dimensional systems, with a focus on uniformly expanding coupled dynamics. Discover how Tanzi quantifies this relationship and demonstrates that, under certain conditions, an equilibrium state of the thermodynamic limit can describe the statistical behavior of the finite system for remarkably long transients, scaling exponentially with the number of coupled units. Gain insights into this complex topic presented at IPAM's "Reconstructing Network Dynamics from Data: Applications to Neuroscience and Beyond" workshop.