Author:
Temčinas Tadas,Nanda Vidit,Reinert Gesine
Abstract
AbstractMotivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random vectors which arise organically in the study of random clique complexes. These are:
the vector of critical simplex counts attained by a lexicographical Morse matching,
the vector of simplex counts in the link of a fixed simplex, and
the vector of total simplex counts.
The first of these random vectors forms a cornerstone of modern homology algorithms, while the second one provides a natural generalisation for the notion of vertex degree, and the third one may be viewed from the perspective of U-statistics. To obtain distributional approximations for these random vectors, we extend the notion of dissociated sums to a multivariate setting and prove a new central limit theorem for such sums using Stein’s method.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology
Cited by
1 articles.
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1. Advances in random topology;Journal of Applied and Computational Topology;2024-08-07