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The limit shape of random permutations with polynomially growing cycle weights

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<mark>Journal publication date</mark>2015
<mark>Journal</mark>Latin American Journal of Probability and Mathematical Statistics
Issue number2
Volume12
Number of pages29
Pages (from-to)971-999
Publication StatusPublished
<mark>Original language</mark>English

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 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