We prove that any unconditional set in RN that is invariant under cyclic shifts of coordinates is rigid in ₚN, 1≤ p≤ 2, i.e. it can not be well approximated by linear spaces of dimension essentially smaller than N. We apply the approach of E.D. Gluskin to the setting of average Kolmogorov widths of unconditional random vectors. This paper continues the study of the rigidity initiated by the first author. This research is related to the notion of matrix rigidity developed within Complexity Theory.
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Malykhin et al. (2024) studied this question.
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