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

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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