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arXiv · 2609.10474

MaxCut for $\mathrm{MTP}_2$ Covariances

Gleb Smirnov
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Abstract

Let $X=(X_1,\dots,X_n)\in\{0,1\}^n$ have a multivariate totally positive ($\mathrm{MTP}_2$) law. We prove that $$ \sum_{i<j}\mathbb{E}\left[\left|\mathrm{Cov}(X_i,X_j \mid X_{[n]\setminus\{i,j\}})\right|\right] \le n/2, $$ and more generally a weighted MaxCut inequality for the fully conditioned covariances. As an application, we confirm a conjecture of Allen and O'Donnell on correlation rounding for signed $\mathrm{MTP}_2$ laws.

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Gleb Smirnov. 2026-09-09. MaxCut for $\mathrm{MTP}_2$ Covariances. https://arxiv.org/abs/2609.10474

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