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- W4289916497 abstract "We show that a sequence has effective Hausdorff dimension 1 if and only if it is coarsely similar to a Martin-L{o}f random sequence. More generally, a sequence has effective dimension $s$ if and only if it is coarsely similar to a weakly $s$-random sequence. Further, for any $s<t$, every sequence of effective dimension $s$ can be changed on density at most $H^{-1}(t)-H^{-1}(s)$ of its bits to produce a sequence of effective dimension $t$, and this bound is optimal." @default.
- W4289916497 created "2022-08-06" @default.
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- W4289916497 date "2017-09-15" @default.
- W4289916497 modified "2023-09-30" @default.
- W4289916497 title "Dimension 1 sequences are close to randoms" @default.
- W4289916497 doi "https://doi.org/10.48550/arxiv.1709.05266" @default.
- W4289916497 hasPublicationYear "2017" @default.
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