Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences

Nitya Mani; Dan Mikulincer

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arXiv · 2403.14068

Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences

Nitya Mani·Dan Mikulincer

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Abstract

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.

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Nitya Mani, Dan Mikulincer. 2024-03-21. Characterizing the fourth-moment phenomenon of monochromatic subgraph counts via influences. https://arxiv.org/abs/2403.14068

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