Title: “Logarithmic correlation functions in 2D critical percolation”

Abstract: It is believed that the large-scale geometric properties of 2D critical percolation are described by a logarithmic conformal field theory, but it has been challenging to exhibit concrete examples of logarithmic singularities and to find an explanation and a physical interpretation, in terms of lattice observables, for their appearance. We show that certain percolation correlation functions receive independent contributions from a large number of similar connectivity events happening at different scales. Combined with scale invariance, this leads to logarithmic divergences. Our results provide support for the validity of a CFT description of critical percolation and a step in the direction of a mathematically rigorous formulation of a logarithmic CFT of 2D critical percolation. This talk is based on a joint work with Federico Camia.