On rates of convergence in the Curie-Weiss-Potts model with external field

Abstract

In the present paper we obtain rates of convergence for the limit theorems of the density vector in the Curie-Weiss-Potts model via Stein's Method of exchangeable pairs. Our results include Kolmogorov bounds for multivariate normal approximation in the whole domain $\beta \ge 0$ and $h\ge 0$, where $\beta$ is the inverse temperature and $h$ an exterior field. In this model, the critical line $\beta ={\beta }_c(h)$ is explicitly known and corresponds to a first order transition. We include rates of convergence for non-Gaussian approximations at the extremity of the critical line of the model.

35 pages; the paper now includes bounds for non-smooth test functions