Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 17 (2012), paper no. 16, 11 pp.
Universality of asymptotically Ewens measures on partitions
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.
Electron. Commun. Probab., Volume 17 (2012), paper no. 16, 11 pp.
Accepted: 23 April 2012
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
This work is licensed under a Creative Commons Attribution 3.0 License.
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