AISM 54, 607-620
© 2002 ISM
(Received June 16, 2000; revised February 16, 2001)
Abstract. The Ewens sampling formula in population genetics can be viewed as a probability measure on the group of permutations of a finite set of integers. Functional limit theory for processes defined through partial sums of dependent variables with respect to the Ewens sampling formula is developed. Techniques from probabilistic number theory are used to establish necessary and sufficient conditions for weak convergence of the associated dependent process to a process with independent increments. Not many results on the necessity part are known in the literature.
Key words and phrases: Random partitions, cycle, population genetics, permutations, law of large numbers, probabilistic number theory, Skorohod topology, slowly varying function, functional limit theorem.
Source (TeX , DVI )