Convergence Rate in The Central Limit Theorem for The Curie-Weiss-Potts Model

Abstract

There is a long tradition in considering mean-field models in statistical mechanics. The Curie-Weiss-Potts model is famous, since it exhibits a number of properties of real substances, such as multiple phases, metastable states and others, explicitly. The aim of this paper is to prove Berry-Esseen bounds for the sums of the random variables occurring in a statistical mechanical model called the Curie-Weiss-Potts model or mean-field Potts model. To this end, we will apply Stein?s method using exchangeable pairs. The aim of this thesis is to calculate the convergence rate in the central limit theorem for the Curie-Weiss-Potts model. In chapter 1, we will give an introduction to this problem. In chapter 2, we will introduce the Curie-Weiss-Potts model, including the Ising model and the Curie-Weiss model. Then we will give some results about the phase transition of the Curie-Weiss-Potts model. In chapter 3, we state Stein?s method first, then give the Stein operator and an approximation theorem. In section 4 of this chapter, we will give an application of Stein?s method. In chapter, we will state the main result of this thesis and prove it.