A short survey of Stein's method

TL;DR

This paper surveys the development and recent advances of Stein's method, introduces a generalized perturbative approach, and discusses potential open problems in probability theory.

Contribution

It provides a comprehensive overview of Stein's method, introduces a new generalized perturbative variant, and explores its applications and open problems.

Findings

Overview of Stein's method history and recent progress

Introduction of a generalized perturbative approach

Application to minimal spanning trees

Abstract

Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's method and some recent advances. This is followed by a description of a "general purpose" variant of Stein's method that may be called the generalized perturbative approach, and an application of this method to minimal spanning trees. The article concludes with the descriptions of some well known open problems that may possibly be solved by the perturbative approach or some other variant of Stein's method.