Zero biasing and growth processes

TL;DR

This paper adapts zero biasing techniques to analyze growth processes, deriving central limit theorems with explicit error bounds for specific statistics in combinatorial and urn models.

Contribution

It introduces a general framework using zero biasing for growth process analysis and applies it to obtain quantitative CLTs for Jack measure statistics and urn processes.

Findings

Established CLTs with explicit error bounds for Jack measure statistics.

Derived CLTs with explicit error bounds for Polya-Eggenberger urn process.

Demonstrated the versatility of zero biasing in growth process analysis.

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.