Towards ﬁnding hay in a haystack: explicit tensors of border rank greater than 2.02m in ℂm ⊗ ℂm ⊗ ℂm
Joseph Landsberg and Mateusz Michałek
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Submission date: 02. Jan. 2020
MSC-Numbers: 15A69, 14L35, 68Q15
Link to arXiv: See the arXiv entry of this preprint.
We write down an explicit sequence of tensors in ℂm ⊗ ℂm ⊗ ℂm, 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.