Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein–Tikhomirov method

Eichelsbacher, Peter; Rednoß, Benedikt

doi:10.3150/22-bej1522

Bernoulli

2023

DOI: 10.3150/22-bej1522

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Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein–Tikhomirov method

Peter Eichelsbacher

Benedikt Rednoß

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Cited by 2 publications

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Multivariate central limit theorems for random clique complexes

Temčinas,

Nanda,

Reinert

2023

J Appl. and Comput. Topology

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Motivated 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.

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Multivariate central limit theorems for random clique complexes

Temčinas,

Nanda,

Reinert

2023

J Appl. and Comput. Topology

View full text Add to dashboard Cite

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Normal approximation of subgraph counts in the random-connection model

Liu,

Privault

2024

Bernoulli

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Kolmogorov bounds for decomposable random variables and subgraph counting by the Stein–Tikhomirov method

Cited by 2 publications

References 19 publications

Multivariate central limit theorems for random clique complexes

Multivariate central limit theorems for random clique complexes

Normal approximation of subgraph counts in the random-connection model

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