An arithmetic model for the total disorder process

  • C. P. HughesEmail author
  • A. Nikeghbali
  • M. Yor


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.


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

Mathematics Subject Classification (2000)

60F05 60G15 11M06 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of YorkHeslington, YorkUK
  2. 2.Institut für MathematikUniversität ZürichZurichSwitzerland
  3. 3.Laboratoire de Probabilités et Modéles AléatoiresUniversité Pierre et Marie Curie, et C.N.R.S. UMR 7599ParisFrance

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