WIAS Preprint No. 1922, (2014)

Fluctuations near the limit shape of random permutations under a conservative measure



Authors

  • Cipriani, Alessandra
  • Zeindler, Dirk

2010 Mathematics Subject Classification

  • 60F05 60F10 60F17

Keywords

  • random permutation, multiplicative measure, algebraically growing cycle weights, limit shape, functional central limit theorem, saddle point method

DOI

10.20347/WIAS.PREPRINT.1922

Abstract

In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set {1, ... n} under a particular class of multiplicative measures. Our method is based on generating functions and complex analysis (saddle point method). We show that fluctuations near a point behave like a normal random variable and that the joint fluctuations 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.

Appeared in

  • ALEA, Lat. Am. J. Probab. Math. Stat. 12:2 (2015), pp. 971--999, changed title: The limit shape of random permutations with polynomially growing cycle weights.

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