The limit shape of random permutations with polynomially growing cycle weights

Cipriani, Alessandra and Zeindler, Dirk (2015) The limit shape of random permutations with polynomially growing cycle weights. Latin American Journal of Probability and Mathematical Statistics, 12 (2). pp. 971-999. ISSN 1980-0436

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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

Item Type:
Journal Article
Journal or Publication Title:
Latin American Journal of Probability and Mathematical Statistics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2613
Subjects:
ID Code:
71368
Deposited By:
Deposited On:
22 Oct 2014 08:00
Refereed?:
Yes
Published?:
Published
Last Modified:
05 Jul 2020 04:12