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2012 Universality of asymptotically Ewens measures on partitions
James Zhao
Author Affiliations +
Electron. Commun. Probab. 17: 1-11 (2012). DOI: 10.1214/ECP.v17-1956


We give a criterion for functionals of partitions to converge to a universal limit under a class of measures that "behaves like" the Ewens measure. Various limit theorems for the Ewens measure, most notably the Poisson-Dirichlet limit for the longest parts, the functional central limit theorem for the number of parts, and the Erdos-Turan limit for the product of parts, extend to these asymptotically Ewens measures as easy corollaries. Our major contributions are: (1) extending the classes of measures for which these limit theorems hold; (2) characterising universality by an intuitive and easily-checked criterion; and (3) providing a new and much shorter proof of the limit theorems by taking advantage of the Feller coupling.


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James Zhao. "Universality of asymptotically Ewens measures on partitions." Electron. Commun. Probab. 17 1 - 11, 2012.


Accepted: 23 April 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1246.60041
MathSciNet: MR2915662
Digital Object Identifier: 10.1214/ECP.v17-1956

Primary: 60F05
Secondary: 60C05

Keywords: central limit theorem , Erdos-Turan theorem , Ewens sampling formula , Feller coupling , Logarithmic combinatorial structures , perturbation , Poisson-Dirichlet limit


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