Normal approximation for statistics of randomly weighted complexes

Article Type

Research Article

Publication Title

Electronic Journal of Probability

Abstract

We prove normal approximation bounds for statistics of randomly weighted (simplicial) complexes. In particular, we consider the complete d-dimensional complex on n vertices with d-simplices equipped with i.i.d. weights. Our normal approximation bounds are quantified in terms of stabilization of difference operators, i.e., the effect on the statistic under addition/deletion of simplices. Our proof is based on Chatterjee’s normal approximation bound and is a higher-dimensional analogue of the work of Cao on sparse Erdős–Rényi random graphs but our bounds are more in the spirit of ‘quantitative two-scale stabilization’ bounds by Lachièze-Rey, Peccati, and Yang. As applications, we prove a CLT for nearest face-weights in randomly weighted d-complexes and give a normal approximation bound for local statistics of random d-complexes.

DOI

10.1214/24-EJP1184

Publication Date

1-1-2024

Comments

Open Access; Gold Open Access; Green Open Access

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