Deviation from equidistance for one-dimensional sequences
For a finite sequence ( x i ) i = 1 N in the unit interval, we introduce the gap ratio function which measures the size of the maximal gap length relative to all other gap lengths. This function (asymptotically) captures a lot of information about the degree of uniformity of the sequence. We discuss...
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| Veröffentlicht in: | Aequationes mathematicae 2023-08, Vol.97 (4), p.683-705 |
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| container_end_page | 705 |
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| container_issue | 4 |
| container_start_page | 683 |
| container_title | Aequationes mathematicae |
| container_volume | 97 |
| creator | Weiß, Christian |
| description | For a finite sequence
(
x
i
)
i
=
1
N
in the unit interval, we introduce the gap ratio function which measures the size of the maximal gap length relative to all other gap lengths. This function (asymptotically) captures a lot of information about the degree of uniformity of the sequence. We discuss connections to the theories of dispersion, discrepancy, pair correlation statistics and covering numbers. Furthermore, we explicitly calculate the gap ratio function for some important classes of uniformly distributed sequences. |
| doi_str_mv | 10.1007/s00010-023-00958-x |
| format | Article |
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i
=
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N
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(
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)
i
=
1
N
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(
x
i
)
i
=
1
N
in the unit interval, we introduce the gap ratio function which measures the size of the maximal gap length relative to all other gap lengths. This function (asymptotically) captures a lot of information about the degree of uniformity of the sequence. We discuss connections to the theories of dispersion, discrepancy, pair correlation statistics and covering numbers. Furthermore, we explicitly calculate the gap ratio function for some important classes of uniformly distributed sequences.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00010-023-00958-x</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0002-3866-6874</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Aequationes mathematicae, 2023-08, Vol.97 (4), p.683-705 |
| issn | 0001-9054 1420-8903 |
| language | eng |
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| subjects | Analysis Combinatorics Mathematics Mathematics and Statistics Sequences |
| title | Deviation from equidistance for one-dimensional sequences |
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