The limit shape of random permutations with polynomially growing cycle weights

Alessandra Cipriani, Dirk Zeindler

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

In this work we are considering the behaviour of the limit shape of Young diagrams associated to random permutations on the set (1,...,n) under a particular class of multiplicative measures with polynomial growing cycle weights. Our method is based on generating functions and complex analysis (saddle point method). We show that uctuations near a point behave like a normal random variable and that the joint uctuations at different points of the limiting shape have an unexpected dependence structure. We will also compare our approach with the so-called randomization of the cycle counts of permutations and we will study the convergence of the limit shape to a continuous stochastic process.

Original languageEnglish
Pages (from-to)971-999
Number of pages29
JournalAlea
Volume12
Issue number2
Publication statusPublished - 1 Jan 2015
Externally publishedYes

Keywords

  • Algebraically growing cycle weights
  • Functional central limit theorem
  • Limit shape
  • Multiplicative measure
  • Random permutation
  • Saddle point method

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