Limit theorems for non-local functionals of smooth Gaussian fields via quasi-association
Probability
2026-02-26 v2
Abstract
Many classical objects of study related to the geometry/topology of smooth Gaussian fields (e.g., the volume, surface area or Euler characteristic of excursion sets) have a `locality' property which is crucial to their analysis. More recently, progress has been made in studying `non-local' quantities of such fields (e.g., the component/nodal count or the Betti numbers of excursion sets). In this work, we develop a new approach to analysing non-local functionals based on a form of topological quasi-association. We use this to establish a variety of limit theorems for approximately additive functionals on growing domains, including concentration bounds, a quantitative central limit theorem and the law of the iterated logarithm.
Keywords
Cite
@article{arxiv.2601.04002,
title = {Limit theorems for non-local functionals of smooth Gaussian fields via quasi-association},
author = {Michael McAuley},
journal= {arXiv preprint arXiv:2601.04002},
year = {2026}
}