Professor Oded Schramm
"Dynamic percolation, exceptional times, and harmonic analysis of boolean functions"
Abstract: Suppose that each of the vertices in the triangular grid in the plane is "open" with probability 1/2 independently. It is known since the work of Harris (1960) that the set of open sites does not have an infinite connected component. In dynamic percolation, the sites randomly flip between the states open and closed according to independent (Poisson) clocks.
In joint work with Jeff Steif we show that dynamic percolation has a set of exceptional times in which an infinite open connected component exists. This contrasts with the fact that at any fixed time almost surely all components are finite.
One of the tools used is a new inequality relating the Fourier coefficients of a boolean function with the existence of a randomized algorithm that calculates the function but is unlikely to examine any specific input bit.