Limit Profile for the high-temperature Curie-Weiss model

Abstract: In this paper, we consider the Ising model on the complete graph, also known as the Curie-Weiss model, and establish the limit profile of the Glauber dynamics in the high-temperature regime. Our strategy is a two-dimensional analog of the method developed by Olesker-Taylor and Schmid for the Bernoulli-Laplace urn: The two-coordinate chain associated to the model evolves near-deterministically until just before the cutoff window, while afterwards it approximates a two-dimensional diffusion.