On irreducible central limit theorems
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909965594132480 |
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| author | Caravenna, Francesco Cottini, Francesca Peccati, Giovanni |
| author_facet | Caravenna, Francesco Cottini, Francesca Peccati, Giovanni |
| contents | We consider sequences of homogeneous sums based on independent random variables and satisfying a central limit theorem (CLT). We address the following question: "In which cases is it not possible to reduce such an asymptotic result to the classical Lindeberg-Feller CLT through a restriction of the summation domain?". We provide several sufficient conditions for such irreducibility, expressed both in terms of (hyper)graphs Laplace eigenvalues, and of a certain notion of combinatorial dimension. Our analysis combines Cheeger-type inequalities with fourth moment theorems, showing that the irreducibility of a given CLT for homogeneous sums can be naturally encoded by the connectivity properties of the associated sequence of weighted hypergraphs. Several ad-hoc constructions are provided in the special case of quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00748 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On irreducible central limit theorems Caravenna, Francesco Cottini, Francesca Peccati, Giovanni Probability 60F05, 60C05, 05C40 We consider sequences of homogeneous sums based on independent random variables and satisfying a central limit theorem (CLT). We address the following question: "In which cases is it not possible to reduce such an asymptotic result to the classical Lindeberg-Feller CLT through a restriction of the summation domain?". We provide several sufficient conditions for such irreducibility, expressed both in terms of (hyper)graphs Laplace eigenvalues, and of a certain notion of combinatorial dimension. Our analysis combines Cheeger-type inequalities with fourth moment theorems, showing that the irreducibility of a given CLT for homogeneous sums can be naturally encoded by the connectivity properties of the associated sequence of weighted hypergraphs. Several ad-hoc constructions are provided in the special case of quadratic forms. |
| title | On irreducible central limit theorems |
| topic | Probability 60F05, 60C05, 05C40 |
| url | https://arxiv.org/abs/2510.00748 |