Author:
Briët Jop,Castro-Silva Davi
Abstract
Motivated by a problem in computational complexity, we consider the behavior of rank functions for tensors and polynomial maps under random coordinate restrictions. We show that, for a broad class of rank functions called \emph{natural rank functions}, random coordinate restriction to a dense set will typically reduce the rank by at most a constant factor.
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1. Random restrictions of high-rank tensors and polynomial maps;Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications;2023