Universality of Asymptotically Ewens Measures on Partitions

Details Universality of Asymptotically Ewens Measures on Partitions Universality of Asymptotically Ewens Measures on Partitions

2011-05-05

arxiv.org/abs/1105.1010v2

Electron. Commun. Probab. 17 (2012) no. 16 pp. 1-11

Mathematics

Probability

Scientific paper

We introduce a universality theorem for functionals of measures on partitions which "behave 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 a single, easily-checked criterion; and (3) greatly shortening the proofs of the limit theorems using the Feller coupling.

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