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.
Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes
Applied Algebraic Topology Network via YouTube
Overview
Syllabus
Introduction
Motivation
Torahs Complex
Poisson process
Discussion
First result
Other cases
Other examples
Weak convergence
Score Ahad space
Question
Thermodynamic regime
Intuition
Uniform convergence
Functional central limit theorem
Euler characteristic process
Data analysis
Questions
Taught by
Applied Algebraic Topology Network
