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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.
Original language  English 

Pages (fromto)  635650 
Journal  Random Structures and Algorithms 
Volume  46 
Issue number  4 
Early online date  30 Oct 2013 
DOIs  
Publication status  Published  1 May 2015 
Keywords
 Random permutations
 local limit theorem
 condensing wave
 gamma distribution
 generalised Ewens distribution
 cycle weights
 cycle structure
 BoseEinstein condensation
 random partitions
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Dive into the research topics of 'Cycle length distributions in random permutations with diverging cycle weights'. Together they form a unique fingerprint.Projects
 1 Finished

Emergence of Condensation in Stochastic Systems
Morters, P.
Engineering and Physical Sciences Research Council
1/08/13 → 31/08/16
Project: Research council