On the law of the iterated logarithm for the discrepancy of \(\langle n_kx\rangle\)

DOI10.1007/s00605-008-0549-xzbMath1208.11090OpenAlexW2072971673MaRDI QIDQ1027746

Christoph Aistleitner, István Berkes

Publication date: 30 June 2009

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-008-0549-x

zbMATH Keywords

law of the iterated logarithmdiscrepancysubexponential growthHadamard gap

Mathematics Subject Classification ID

Strong limit theorems (60F15) Irregularities of distribution, discrepancy (11K38)

Related Items (6)

On the central limit theorem for \(f(n_{k}x)\) ⋮ Diophantine equations and the LIL for the discrepancy of sublacunary sequences ⋮ A metric discrepancy result for a lacunary sequence with small gaps ⋮ Covering numbers, dyadic chaining and discrepancy ⋮ A law of the iterated logarithm for discrepancies: non-constant limsup ⋮ PROBABILITY AND METRIC DISCREPANCY THEORY

Cites Work

• The law of the iterated logarithm for discrepancies of \(\{\theta^{n}x\}\)
• Moment and probability bounds with quasi-superadditive structure for the maximum partial sum
• An almost sure invariance principle for lacunary trigonometric series
• A metrical result on the discrepancy of (nα)
• Empirical Distribution Functions and Strong Approximation Theorems for Dependent Random Variables. A Problem of Baker in Probabilistic Number Theory
• An asymptotic property of a gap sequence
• Probability methods in some problems of analysis and number theory

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