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PreprintCC BY 4.0arXiv

MaxCut for MTP2 Covariances

  • Gleb Smirnov
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Abstract

Let X=(X1,…,Xn)∈{0,1}n have a multivariate totally positive (MTP2) law. We prove that βˆ‘i<j𝔼[|Cov(Xi,Xj | X[n]βˆ–{i,j})|] ≀ 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 MTP2 laws.

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Cite

BibTeXRIS
BibTeX
@misc{smirnov2026maxcut,
  title = {{MaxCut for $\mathrmMTP_2$ Covariances}},
  author = {Gleb Smirnov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10474},
  eprint = {2609.10474},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10474},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - MaxCut for MTP_2 Covariances
AU  - Gleb Smirnov
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10474
UR  - https://arxiv.org/abs/2609.10474
AB  - Let X=(X_1,…,X_n)∈{0,1}^n have a multivariate totally positive (MTP_2) law. We prove that βˆ‘_i<j𝔼[|Cov(X_i,X_j | X_[n]βˆ–{i,j})|] ≀ 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 MTP_2 laws.
ER  -