Discrete Mathematics and Optimization Seminar
Dec. 9th, 2010
MC103, 4-5PM
Continuum Percolation is Noise Sensitive
Simon Griffiths
IMPA, Rio de Janeiro
If you can see 99% of a picture you should still be able to make out the image. If you count 99% of the votes in an election you should be pretty sure of the eventual outcome. A system is Noise Sensitive if the opposite is true, i.e. if knowing 99% of the information is useless. In a seminal paper a decade ago Benjamini, Kalai and Schramm proved that the crossing event in site percolation on the triangular lattice is Noise Sensitive. We give an overview of their proof and discuss the connection of their work to the startling results for dynamic percolation of Schramm and Steif. We then discuss how their methods can be adapted to prove that Continuum Percolation is Noise Sensitive.

(joint with Daniel Ahlberg, Erik Broman and Robert Morris)