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

2020/02/22 by Johannes Krebs, Krebs, Johannes
Computer Science · Mathematics · #60F15 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Statistics Theory (math.ST) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2002.09764

openalex publication_date 2020/02/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We study the law of the iterated logarithm (Khinchin (1924), Kolmogorov\n(1929)) and related strong invariance principles in stochastic geometry. As\npotential applications, we think of well-known functionals such as functionals\ndefined on the k-nearest neighbors graph and important functionals in\ntopological data analysis such as the Euler characteristic and persistent Betti\nnumbers.\n

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