Limit theorems for non-local functionals of smooth Gaussian fields via quasi-association
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917294253277184 |
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| author | McAuley, Michael |
| author_facet | McAuley, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04002 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit theorems for non-local functionals of smooth Gaussian fields via quasi-association McAuley, Michael Probability 60G60 (Primary) 60G15, 60K35 (Secondary) 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. |
| title | Limit theorems for non-local functionals of smooth Gaussian fields via quasi-association |
| topic | Probability 60G60 (Primary) 60G15, 60K35 (Secondary) |
| url | https://arxiv.org/abs/2601.04002 |