We study random permutations of n objects with respect to multiplicative measures with polynomial growing cycle weights. We determine in this paper the asymptotic behavior of the long cycles under this measure and also prove that the cumulative cycle numbers converge in the region of the long cycles to a Poisson process.

中文翻译：

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长周期的随机排列具有多项式增长的循环权重

我们研究与多项式增长周期权重相乘的n个对象的随机排列。我们在本文中确定了在这种情况下长周期的渐近行为，并证明了累积周期数在长周期区域内收敛到Poisson过程。