# Non-Asymptotic Concentration of Magnetization in the Curie-Weiss Model at Subcritical Temperatures

## TL;DR

This paper establishes non-asymptotic concentration bounds for the magnetization in the Curie-Weiss model at subcritical temperatures and derives a diffusion limit theorem for the scaled magnetization under a Metropolis-Hastings algorithm.

## Contribution

It provides new non-asymptotic concentration results and a diffusion limit theorem for the magnetization at subcritical temperatures, complementing existing results at other temperature regimes.

## Key findings

- Non-asymptotic concentration bounds for magnetization
- Diffusion limit theorem for scaled magnetization
- Results specific to subcritical temperature regime

## Abstract

In this short paper, we obtain non-asymptotic concentration results for magnetization of the Curie-Weiss model at subcritical temperatures, which leads to a diffusion limit theorem of the scaled and centered magnetization driven by a Metropolis-Hasting algorithm. These results are complementary to results at supercritical and critical temperatures in Bierkens et al (2017).