Analysis and Probability Seminar

The fuzzy Potts model is obtained by independently coloring the clusters of a Fortuin-Kasteleyn (FK) percolation. We study the model on the square lattice when the FK percolation is critical. Under the assumption that this critical FK percolation converges to a conformally invariant scaling limit (which is known to hold for the FK-Ising model), we show that the obtained coloring converges to variants of Conformal Loop Ensembles constructed, described and studied by Miller, Sheffield and Werner. Using discrete considerations, we also show that the arm exponents for this coloring in the discrete model are identical to the ones of the continuum model. This allows us to determine the arm exponents for the planar fuzzy Potts model.

Joint work with Matthis Lehmkuehler.