The limit shape of random permutations with polynomially growing cycle weights
Abstract
In this work we are considering the behavior of the limit shape of Young diagrams associated to random permutations on the set 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.
Cite
@article{arxiv.1312.3517,
title = {The limit shape of random permutations with polynomially growing cycle weights},
author = {Alessandra Cipriani and Dirk Zeindler},
journal= {arXiv preprint arXiv:1312.3517},
year = {2014}
}
Comments
36 pages, 3 figures. The paper was subject to a major revision (compared to v1): 1) we considered more general weights, i. e. $\theta_m= (\log m)^j m^\alpha$, 2) title replaced, 3) improvements of the presentation, 4) correction of typos and minor mathematical errors