Deviation from equidistance for one-dimensional sequences
نویسندگان
چکیده
Abstract For a finite sequence $$(x_i)_{i=1}^N$$ ( x i ) = 1 N in the unit interval, we introduce gap ratio function which measures size of maximal length relative to all other lengths. This (asymptotically) captures lot information about degree uniformity sequence. We discuss connections theories dispersion, discrepancy, pair correlation statistics and covering numbers. Furthermore, explicitly calculate for some important classes uniformly distributed sequences.
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ژورنال
عنوان ژورنال: Aequationes Mathematicae
سال: 2023
ISSN: ['0001-9054', '1420-8903']
DOI: https://doi.org/10.1007/s00010-023-00958-x