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  • 1 Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
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Abstract

This paper is mainly concerned with the limit distribution of on the unit interval when the increasing sequence {nk} has bounded gaps, i.e., 1≤nk+1nk=O(1). By Bobkov–Götze [4], it was proved that the limiting variance must be less than 1/2 in this case. They proved that the centered Gaussian distribution with variance 1/4 together with mixtures of Gaussian distributions belonging to a huge class can be limit distributions. In this paper it is proved that any Gaussian distribution with variance less than 1/2 can be a limit distribution.

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  • SJR Quartile Score (2019): Q2 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.538
  • Scimago Journal Rank (2018): 0.488
  • SJR Hirsch-Index (2018): 36
  • SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Acta Mathematica Hungarica
Language English
Size B5
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Foundation
1950
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3
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6
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)