Probability Seminar: Gordon Slade

The sharpness of the percolation phase transition, which is a crucial and much cited element of the theory, was first proved independently by Menshikov in 1986 and by Aizenman and Barsky in 1987. On February 11, 2015, a remarkable new proof was posted on arXiv by Duminil-Copin and Tassion.  I will describe their proof, which is completed in two pages, in its entirety.