On the law of the iterated logarithm and strong invariance principles in stochastic geometry

02/22/2020

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by   Johannes Krebs, et al.

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We study the law of the iterated logarithm (Khinchin (1933), Kolmogorov (1929)) and related strong invariance principles in stochastic geometry. As potential applications, we think of well-known functionals such as functionals defined on the k-nearest neighbors graph and important functionals in topological data analysis such as the Euler characteristic and persistent Betti numbers.