Cycle length distributions in random permutations with diverging cycle weights
Steffen Dereich, Peter Mörters · Random Structures and Algorithms · 2013
Abstract 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