Universality of Asymptotically Ewens Measures on Partitions
Probability
2012-04-25 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1105.1010,
title = {Universality of Asymptotically Ewens Measures on Partitions},
author = {James Y. Zhao},
journal= {arXiv preprint arXiv:1105.1010},
year = {2012}
}