Lecture - online event

Abstract: One of the most prominent phenomena in percolation theory (and more generally, in statistical physics) is the so called sharpness of phase transition: the abrupt change of behavior from a strongly non-percolative (disordered) regime straight to a strongly percolative (ordered) one. For the classical example of Bernoulli (independent) percolation, subcritical sharpness was proved independently by Menshikov (1986) and Aizenman and Barsky (1987), whereas supercritical sharpness was obtained by Grimmett and Marstrand (1990). Since then, proving similar results for more general (dependent) percolation models became a very active field of research in percolation theory, which led to great progress in the last decade. In this talk we shall give a brief overview of the field and describe a recently developed approach based on an interpolation scheme aimed at integrating out the long-range dependence of the model .