Zero biasing and growth processes

Abstract

The tools of zero biasing are adapted to yield a general result suitable for analyzing the behavior of certain growth processes. The main theorem is applied to prove central limit theorems, with explicit error terms in the L^1 metric, for certain statistics of the Jack measure on partitions and for the number of balls drawn in a Polya-Eggenberger urn process.Comment: 21 pages. Error in one term of the bound of the main theorem has been corrected, resulting in some changes to the bound for urn proces