On trigonometric sums with random frequencies

Alina Bazarova, I. Berkes, Marko Raseta

Research output: Contribution to journalArticle

Abstract

We prove that if Ik are disjoint blocks of positive integers and nk are independent random variables on some probability space (Ω, F, P) such that nk is uniformly distributed on Ik, then N N1/2 (sin 2πnkx − E(sin 2πnkx)) k=1 has, with P-probability 1, a mixed Gaussian limit distribution relative to the probability space ((0, 1), B, λ), where B is the Borel σ-algebra and λ is the Lebesgue measure. We also investigate the case when nk have continuous uniform distribution on disjoint intervals Ik on the positive axis.

Original languageEnglish
Pages (from-to)141-152
Number of pages12
JournalStudia Scientiarum Mathematicarum Hungarica
Volume55
Issue number1
DOIs
Publication statusPublished - Mar 1 2018

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Trigonometric Sums
Probability Space
Continuous uniform distribution
Disjoint
Limit Distribution
Independent Random Variables
Lebesgue Measure
Gaussian distribution
Algebra
Interval
Integer

Keywords

  • Central limit theorem
  • Random gaps
  • Trigonometric sums

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On trigonometric sums with random frequencies. / Bazarova, Alina; Berkes, I.; Raseta, Marko.

In: Studia Scientiarum Mathematicarum Hungarica, Vol. 55, No. 1, 01.03.2018, p. 141-152.

Research output: Contribution to journalArticle

Bazarova, Alina ; Berkes, I. ; Raseta, Marko. / On trigonometric sums with random frequencies. In: Studia Scientiarum Mathematicarum Hungarica. 2018 ; Vol. 55, No. 1. pp. 141-152.
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