Statistics Seminars: Noise sensitivity in continuum percolation
12 December 2011 14:00 in CM221
We shall discuss recent results concerning Noise Sensitivity of Boolean functions and in particular Noise Sensitivity in Percolation. Since the subject was introduced, and the Noise Sensitivity of various discrete Percolation models proved by Bejamini, Kalai and Schramm in 1999, there have been a number of articles proving sharper and sharper results that allow one to prove the existence of exceptional times in Dynamic Percolation.
In this talk we discuss Noise Sensitivity in Continuum Percolation.
We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first for which the critical probability p_c \ne 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures.
(Joint with Daniel Ahlberg, Erik Broman and Robert Morris.)
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