Electronic Communications in Probability

Universality of asymptotically Ewens measures on partitions

James Zhao

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 17 (2012), paper no. 16, 11 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263149

Digital Object Identifier
doi:10.1214/ECP.v17-1956

Mathematical Reviews number (MathSciNet)
MR2915662

Zentralblatt MATH identifier
1246.60041

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60C05: Combinatorial probability

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

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Zhao, James. Universality of asymptotically Ewens measures on partitions. Electron. Commun. Probab. 17 (2012), paper no. 16, 11 pp. doi:10.1214/ECP.v17-1956. https://projecteuclid.org/euclid.ecp/1465263149


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