A central limit theorem via differential equations

TL;DR

This paper extends Wormald's differential equations method to establish a central limit theorem, demonstrating that certain parameters in discrete random processes converge to a multivariate normal distribution under specific conditions.

Contribution

It introduces additional conditions to Wormald's framework, enabling the derivation of a multivariate normal limit for parameters in discrete random processes.

Findings

Parameters converge to a multivariate normal distribution.

Extension of Wormald's method to probabilistic limit theorems.

Provides criteria for normal convergence in discrete processes.

Abstract

In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further conditions are satisfied, the parameters converge to a multivariate normal distribution.