Abstract: We study the probability that the origin is connected to the sphere of radius R in critical percolation in high dimensions, namely when the dimension d is a large fixed constant, or when d>6 and the lattice is sufficiently spread out. I will present highlights of the proof that this probability decays like R^{-2}.

Joint work with Gady Kozma.

Coffee will be served at 12:00 before the lecture
at Schreiber building 006