# Total variation distance and the Erdős–Turán law for random permutations with polynomially growing cycle weights

@inproceedings{Storm2014TotalVD, title={Total variation distance and the Erdős–Tur{\'a}n law for random permutations with polynomially growing cycle weights}, author={Jesper Storm and Dirk Zeindler}, year={2014} }

- Published 2014
DOI:10.1214/15-aihp692

We study the model of random permutations of $n$ objects with polynomially growing cycle weights, which was recently considered by Ercolani and Ueltschi, among others. Using saddle-point analysis, we prove that the total variation distance between the process which counts the cycles of size $1, 2, ..., b$ and a process $(Z_1, Z_2, ..., Z_b)$ of independent Poisson random variables converges to $0$ if and only if $b=o(\ell)$ where $\ell$ denotes the length of a typical cycle in this model. By… CONTINUE READING

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## The order of large random permutations with cycle weights

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