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math.PR2020
On approximation theorems for the Euler characteristic with applications to the bootstrap
Johannes Krebs, Benjamin Roycraft, Wolfgang Polonik
We study approximation theorems for the Euler characteristic of the Vietoris-Rips and Cech filtration. The filtration is obtained from a Poisson or binomial sampling scheme in the…
math.PR2020
On the law of the iterated logarithm and strong invariance principles in stochastic geometry
Johannes Krebs
We study the law of the iterated logarithm (Khinchin (1924), Kolmogorov (1929)) and related strong invariance principles in stochastic geometry. As potential applications, we think…