# Jerusalem Mathematics Colloquium

Thursday, 23rd December 2004, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Oded Schramm

(Microsoft)

"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.

Light refreshments will be served in the faculty lounge at 3:30.

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