Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02m$ in $C^m\otimes C^m\otimes C^m$

J. M. Landsberg; Mateusz Michałek

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arXiv · 1912.11927

Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02m$ in $C^m\otimes C^m\otimes C^m$

J. M. Landsberg·Mateusz Michałek

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Abstract

We write down an explicit sequence of tensors in $C^m\otimes C^m\otimes C^m$, for all $m$ sufficiently large, having border rank at least $2.02m$, overcoming a longstanding barrier. We obtain our lower bounds via the border substitution method.

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J. M. Landsberg, Mateusz Michałek. 2019-12-26. Towards finding hay in a haystack: explicit tensors of border rank greater than $2.02m$ in $C^m\otimes C^m\otimes C^m$. https://arxiv.org/abs/1912.11927

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