Showing math.PRShow all
3 papers · 1 filter
math.PR2020
Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds
Andrew M. Thomas, Takashi Owada
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric complexes whose points lie in t…
math.PR2019
Functional limit theorems for the Euler characteristic process in the critical regime
Andrew M. Thomas, Takashi Owada
This study presents functional limit theorems for the Euler characteristic of Vietoris-Rips complexes. The points are drawn from a non-homogeneous Poisson process on …
math.PR2018
Limit theorems for process-level Betti numbers for sparse, critical, and Poisson regimes
Takashi Owada, Andrew Thomas
The objective of this study is to examine the asymptotic behavior of Betti numbers of Čech complexes treated as stochastic processes and formed from random points in the -dimens…