@article{ECP1956,
author = {James Zhao},
title = {Universality of asymptotically Ewens measures on partitions},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {17},
year = {2012},
keywords = {Ewens sampling formula; Feller coupling; logarithmic combinatorial structures; perturbation; Poisson-Dirichlet limit; central limit theorem; Erdos-Turan theorem},
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.},
pages = {no. 16, 1-11},
issn = {1083-589X},
doi = {10.1214/ECP.v17-1956},
url = {http://ecp.ejpecp.org/article/view/1956}}