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

Abstract

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 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.