We construct a natural (and very surprising) coupling between the critical Ising magnetisation field and the Gaussian free field. We do so by proving convergence in the scaling limit of a novel, analogous coupling for discrete models.
We construct an excursion decomposition of the continuum XOR-Ising model, that more generally applies to the real and imaginary parts of the complex multiplicative chaos of a Gaussian free field. We also prove convergence in the scaling limit of the discrete excursion decomposition.
Published:
One of the four talks part of a minicourse split with Marcin and Lorca, based on our paper with the same title.