Convergence of the Ising-Kac Model to Φ4 in Three Dimensions

Explore a 40-minute lecture on the convergence of the Ising-Kac model to $\Phi^4$ in three dimensions, presented by Hendrik Weber at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI). Delve into the Glauber dynamics on a three-dimensional lattice at near-critical temperature, and discover how these dynamics approximate the parabolic $\varphi^4$ SPDE in a specific parameter regime. Learn about the completion of previous works in one and two spatial dimensions, confirming a conjecture by Giacomin-Lebowitz-Presutti. Gain insights into the technical analysis, which heavily relies on Hairer's theory of regularity structure and the discretisation framework by Erhard and Hairer. Understand the key step involving the construction and analysis of an appropriate model for the discrete particle system. This lecture presents joint work with Paolo Grazieschi (Bath) and Konstantin Matetski (Michigan State).

Hendrik Weber - Convergence of the Ising-Kac model to $\Phi^4$ in three dimensions