172 citations · 377 across the 33 of their papers we have counts for
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math.PR2009★ 172 cited
Random geometric complexes
Matthew Kahle
We study the expected topological properties of Cech and Vietoris-Rips complexes built on i.i.d. random points in R^d. We find higher dimensional analogues of known results for con…
math.MG2009
Sparse stable configurations of hard discs in a box
Matthew Kahle
We construct stable configurations of n overlapping discs of radius r in a unit square, with r = O(1/n). By a result of Diaconis, Lebeau, and Michel, this result is best possible,…