Laboratoire de Physique Théorique
Toulouse - UMR 5152

Random fractals which are conformally invariant often appear in critical statistical models : a well-known example are the clusters of pure (uncorrelated) percolation. The full characterisation of these extended objects is a long-standing problem. For instance, computing the probability that a given set of points belong to the same cluster is an open question, which hints at new ways in which conformal symmetry is implemented, and challenges our understanding on conformal field theory.

In this talk, I will show how the effect of the torus topology on these probabilities allows to access very important information about the CFT underlying a critical statistical model. In particular I will present very recent results about the conformal invariance and the universality classes of long-range correlated random surfaces. If time allows I will discuss how these topological effects enabled also to check conjectures about the CFT describing the clusters of another line of correlated percolation models, the Q-states Potts models.

References : arXiv:1907.11041, arXiv:1912.05865, arXiv:2005.11830