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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2403.14068 |
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| _version_ | 1866916169919758336 |
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| author | Mani, Nitya Mikulincer, Dan |
| author_facet | Mani, Nitya Mikulincer, Dan |
| contents | We investigate the distribution of monochromatic subgraph counts in random vertex $2$-colorings of large graphs. We give sufficient conditions for the asymptotic normality of these counts and demonstrate their essential necessity (particularly for monochromatic triangles). Our approach refines the fourth-moment theorem to establish new, local influence-based conditions for asymptotic normality; these findings more generally provide insight into fourth-moment phenomena for a broader class of Rademacher and Gaussian polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences Mani, Nitya Mikulincer, Dan Probability Combinatorics 60C05 We investigate the distribution of monochromatic subgraph counts in random vertex $2$-colorings of large graphs. We give sufficient conditions for the asymptotic normality of these counts and demonstrate their essential necessity (particularly for monochromatic triangles). Our approach refines the fourth-moment theorem to establish new, local influence-based conditions for asymptotic normality; these findings more generally provide insight into fourth-moment phenomena for a broader class of Rademacher and Gaussian polynomials. |
| title | Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences |
| topic | Probability Combinatorics 60C05 |
| url | https://arxiv.org/abs/2403.14068 |