Dr. Panqiu Xia (University of Cardiff) – Ergodicity and Gaussian fluctuations of stochastic heat equations

In this talk, I will discuss the ergodicity of the stochastic heat equation driven by centred Gaussian noise, which is white in time and coloured in space, satisfying the Dalang condition. I will also provide a sufficient condition for the ergodicity, and classify the invariant measures based on their expectations. Assuming the spatial correlation has a Riesz-type tail of the form $|x|^{- \gamma}$, a Gaussian fluctuation result under diffusive scaling was established. In the case of a heavy tail, specifically when $\gamma < d$, the diffusive scaling limit satisfies an Edwards–Wilkinson equation. This talk is based on joint work with Le Chen, Alex Dunlap, Cheng Ouyang, and Samy Tindel.