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Distance Functions, Critical Points, and Topology for Some Random Complexes
Distance function critical points Morse index Cech complex Poisson process central limit theorem Betti numbers
2011/9/20
Abstract: 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 random. In par...
Limit theorems for Betti numbers of random simplicial complexes
Limit theorems random simplicial complexes
2010/12/9
There have been several recent articles studying homology of various types of random simplicial complexes. Several theorems have concerned thresholds for vanishing of homology, and in some cases expec...