Cycle length distributions in random permutations with diverging cycle weights. Issue 4 (30th October 2013)

• Record Type: Journal Article
• Authors: Dereich, Steffen; Mörters, Peter
• Is Part Of: Random structures & algorithms. Volume 46:Issue 4(2015)
• Page Start: 635
• Page End: 650
• Publication Date: 2013-10-30
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20520
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>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</p> </abstract>