Subspaces of tensors with high analytic rank
It is shown that for any subspace V⊆Fn×⋯×np of d-tensors, if dim(V)≥tnd−1, then there is subspace W⊆V of dimension at least t/(dr)−1 whose nonzero elements all have analytic rank Ωd,p(r). As an application, we generalize a result of Altman on Szemerédi's theorem with random differences.
|Series||arXiv.org e-Print archive|
Briët, J. (2019). Subspaces of tensors with high analytic rank. arXiv.org e-Print archive.