Ritvik Radhakrishnan

We prove a general interpolation formula which, in particular, gives a quantitative and unified proof of the FKG and BK inequalities. We use this to show that in critical bond percolation on the square lattice the two arm exponent is strictly larger than the one arm exponent squared. This answers a question of Schramm and Steif (2010), and shows that their proof of the existence of exceptional times on the triangular lattice also applies to the square lattice. This method also gives a new proof of a result due to Beffara and Nolin (2011) stating that monochromatic arm exponents are strictly larger than polychromatic arm exponents. This talk is based on joint work with Vincent Tassion.