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Cycle length distributions in random permutations with diverging cycle weights
Author(s) -
Dereich Steffen,
Mörters Peter
Publication year - 2015
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/rsa.20520
Subject(s) - mathematics , limit (mathematics) , distribution (mathematics) , combinatorics , random variable , statistical physics , central limit theorem , probability distribution , statistics , mathematical analysis , physics
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