Convergence to Decorated Lévy Processes for Dynamical Systems

Explore a comprehensive lecture on the convergence to decorated Lévy processes for dynamical systems, presented by Jorge Freitas at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into a general framework for weak convergence to decorated Lévy processes in enriched spaces of càdlàg functions for vector-valued processes arising in deterministic systems. Examine applications including uniformly expanding maps with unbounded observables and nonuniformly expanding/hyperbolic maps with bounded observables, such as intermittent maps and dispersing billiards with flat cusps. Discover why convergence fails in all Skorohod topologies for many of these examples and how the enriched space captures details of excursions not recorded by Skorohod or Whitt topologies. This one-hour talk, part of the Workshop on "Rare Events in Dynamical Systems," offers a deep dive into advanced mathematical concepts at the intersection of probability theory and dynamical systems.