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arXiv · 1803.06847

The square negative correlation on l_p^n balls

David Alonso-Gutiérrez·Julio Bernués
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Abstract

In this paper we prove that for any $p\in[2,\infty)$ the $\ell_p^n$ unit ball, $B_p^n$, satisfies the square negative correlation property with respect to every orthonormal basis, while we show it is not always the case for $1\le p\le 2$. In order to do that we regard $B_p^n$ as the orthogonal projection of $B_p^{n+1}$ onto the hyperplane $e_{n+1}^\perp$. We will also study the orthogonal projection of $B_p^n$ onto the hyperplane orthogonal to the diagonal vector $(1,\dots,1)$. In this case, the property holds for all $p\ge 1$ and $n$ large enough.

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David Alonso-Gutiérrez, Julio Bernués. 2018-03-19. The square negative correlation on l_p^n balls. https://arxiv.org/abs/1803.06847

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