Cycle length distributions in random permutations with diverging cycle weights

Steffen Dereich, Peter Morters

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4 Citations (Scopus)
133 Downloads (Pure)

Abstract

We study the model of random permutations with diverging cycle weights, which was recently considered by Ercolani and Ueltschi, and others. Assuming only regular variation of the cycle weights we obtain a very precise local limit theorem for the size of a typical cycle, and use this to show that the empirical distribution of properly rescaled cycle lengths converges in probability to a gamma distribution.
Original languageEnglish
Pages (from-to)635-650
JournalRandom Structures and Algorithms
Volume46
Issue number4
Early online date30 Oct 2013
DOIs
Publication statusPublished - 1 May 2015

Keywords

  • Random permutations
  • local limit theorem
  • condensing wave
  • gamma distribution
  • generalised Ewens distribution
  • cycle weights
  • cycle structure
  • Bose-Einstein condensation
  • random partitions

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