Distance Functions, Critical Points, and the Topology of Random Čech Complexes

Omer Bobrowski, Robert J. Adler

For a finite set of points $P$ in $R^d$, the function $d_P:R^d\to R^{+}$ measures Euclidean distance to the set $P$. We study the number of critical points of $d_P$ when $P$ is a P…