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arXiv · 0908.2217

Random permutations with cycle weights

Volker Betz·Daniel Ueltschi·Yvan Velenik
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Abstract

We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a fraction of $n$ or a logarithmic power of $n$.

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Volker Betz, Daniel Ueltschi, Yvan Velenik. 2009-08-17. Random permutations with cycle weights. https://doi.org/10.1214/10-aap697

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