Stochastic PDEs and Scaling Limits: I

The aim of my mini-course is to show how recently developed techniques from the analysis of singular stochastic PDEs (in particular the theory of regularity structures) can be used to analyse scaling limits of interacting particle systems. In the end I want to explain a new proof of the emergence of the KPZ equation from the weakly asymmetric simple exclusion processes completed recently (arXiv:2505.00621). To this end I will review some of the key ideas from the theory of regularity structures in the context of the KPZ equation and then show how these can be modified to apply in the discrete setting.

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