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



Author: Volker Betz, Daniel Ueltschi, Yvan Velenik

Source: https://arxiv.org/







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