The limit shape of random permutations with polynomially growing cycle weights

Alessandra Cipriani; Dirk Zeindler

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arXiv · 1312.3517

The limit shape of random permutations with polynomially growing cycle weights

Alessandra Cipriani·Dirk Zeindler

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Abstract

In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set $\{1,\dots,n\}$ 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.

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Alessandra Cipriani, Dirk Zeindler. 2013-12-12. The limit shape of random permutations with polynomially growing cycle weights. https://arxiv.org/abs/1312.3517

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