Cycle length distributions in random permutations with diverging cycle weights
Cycle length distributions in random permutations with diverging cycle weights
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DOI：
10.1002/rsa.20520
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发表时间：
2015-07
影响因子：
1
通讯作者：
S. Dereich;Peter Mörters
中科院分区：
文献类型：
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作者：
S. Dereich;Peter Mörters
我们研究了最近Ercolani和Ueltschi等人研究的具有发散循环权的随机置换模型。假设循环权重只有规则的变化，我们得到了一个关于典型循环大小的非常精确的局部极限定理，并用它来证明适当重新标度的循环长度的经验分布在概率上收敛于伽马分布。版权所有©2013 Wiley Permials，Inc.随机结构。2015年，46,635-650
We study the model of random permutations with diverging cycle weights, which was recently considered by Ercolani and Ueltschi, and others. Assuming only regular variation of the cycle weights we obtain a very precise local limit theorem for the size of a typical cycle, and use this to show that the empirical distribution of properly rescaled cycle lengths converges in probability to a gamma distribution.Copyright © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,635–650, 2015