Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes
Explore functional limit theorems for Euler characteristic processes in this 59-minute conference talk. Delve into the analysis of Euler Characteristics of Vietoris-Rips complex filtrations, where underlying points are derived from non-homogeneous Poisson processes in R^d. Examine the critical regime where connectivity radii approach zero but maintain high connectivity and non-trivial topology. Discover strong law of large numbers and central limit theorem results for normalized Euler characteristic processes in Skorohod space. Gain insights into topics such as Torah's Complex, weak convergence, thermodynamic regime intuition, and functional central limit theorems. Conclude with a discussion on practical applications in data analysis and engage in a Q&A session.