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Limit distributions in metric discrepancy theory

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Abstract

Let (n k ) k ≥ 1 be a lacunary sequence of integers, satisfying certain number-theoretic conditions. We determine the limit distribution of \({\sqrt{N} D_N (n_{k} x)}\) as \({N \to \infty}\) , where D N (n k x) denotes the discrepancy of the sequence (n k x) k ≥ 1 mod 1.

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Authors and Affiliations

  1. Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010, Graz, Austria

    Christoph Aistleitner

  2. Institute of Statistics, Graz University of Technology, Münzgrabenstraße 11, 8010, Graz, Austria

    István Berkes

Authors
  1. Christoph Aistleitner
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  2. István Berkes
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Corresponding author

Correspondence to Christoph Aistleitner.

Additional information

Communicated by J. Schoißengeier.

C. Aistleitner’s research supported by FWF grant S9603-N23.

I. Berkes’s research supported by FWF grant S9603-N23 and OTKA grant K 67961.

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Aistleitner, C., Berkes, I. Limit distributions in metric discrepancy theory. Monatsh Math 169, 253–265 (2013). https://doi.org/10.1007/s00605-012-0378-9

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  • DOI: https://doi.org/10.1007/s00605-012-0378-9

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