Omer Bobrowski

A Universal Law of Large Numbers for Extreme Cycles in Random \v{C}ech Complexes

We study the maximal multiplicative persistence of $k$-cycles in random \v{C}ech complexes. Let $f:\mathbb{R}^d\to\mathbb{R}$ be a probability density function, let ${P}_n$ be a Poisson process with intensity $nf$, and let $\Pi_{k,n}$ denote the largest death-to-birth ratio among all non-essential $k$-cycles ($1\le k \...