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An arithmetic model for the total disorder process
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  • Published: 02 June 2007

An arithmetic model for the total disorder process

  • C. P. Hughes1,
  • A. Nikeghbali2 &
  • M. Yor3 

Probability Theory and Related Fields volume 141, pages 47–59 (2008)Cite this article

  • 109 Accesses

  • 10 Citations

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Abstract

We prove a multidimensional extension of Selberg’s central limit theorem for the logarithm of the Riemann zeta function on the critical line. The limit is a totally disordered process, whose coordinates are all independent and Gaussian.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of York, Heslington, York, YO10 5DD, UK

    C. P. Hughes

  2. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zurich, Switzerland

    A. Nikeghbali

  3. Laboratoire de Probabilités et Modéles Aléatoires, Université Pierre et Marie Curie, et C.N.R.S. UMR 7599, 175, rue du Chevaleret, 75013, Paris, France

    M. Yor

Authors
  1. C. P. Hughes
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  2. A. Nikeghbali
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  3. M. Yor
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Corresponding author

Correspondence to C. P. Hughes.

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Cite this article

Hughes, C.P., Nikeghbali, A. & Yor, M. An arithmetic model for the total disorder process. Probab. Theory Relat. Fields 141, 47–59 (2008). https://doi.org/10.1007/s00440-007-0079-9

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  • Received: 07 December 2006

  • Revised: 27 April 2007

  • Published: 02 June 2007

  • Issue Date: May 2008

  • DOI: https://doi.org/10.1007/s00440-007-0079-9

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Keywords

  • Total disorder process
  • Convergence in distribution
  • Central limit theorem
  • Riemann zeta function

Mathematics Subject Classification (2000)

  • 60F05
  • 60G15
  • 11M06
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