Random permutations with logarithmic cycle weights

@article{Robles2018RandomPW,
  title={Random permutations with logarithmic cycle weights},
  author={Nicolas Robles and Dirk Zeindler},
  journal={arXiv: Probability},
  year={2018}
}
We consider random permutations on $\Sn$ with logarithmic growing cycles weights and study the asymptotic behavior as the length $n$ tends to infinity. We show that the cycle count process converges to a vector of independent Poisson variables and also compute the total variation distance between both processes. Next, we prove a central limit theorem for the total number of cycles. Furthermore we establish a shape theorem and a functional central limit theorem for the Young diagrams associated… 
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