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Operator limit of the circular beta ensemble

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 Added by Benedek Valko
 Publication date 2017
  fields
and research's language is English




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We provide a precise coupling of the finite circular beta ensembles and their limit process via their operator representations. We prove explicit bounds on the distance of the operators and the corresponding point processes. We also prove an estimate on the beta-dependence in the $text{Sine}_{beta}$ process.

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