Daniel Ahlberg: Is ‘being above the median’ a noise sensitive property?

Abstract

 A general framework for the study of macroscopic effects of a small perturbation of a statistical system was introduced by Benjamini-Kalai-Schramm in 1999, in terms of Boolean functions. In a loose sense, the system is said to be noise sensitive if the effect of the perturbation can be detected macroscopically. An extensive analysis of noise sensitivity in planar percolation models was carried out in the coming decades. However, for spatial growth processes, such as first-passage percolation, the main observables are not Boolean but real-valued, and would not immediately fit the developed framework. In 2011, Benjamini suggested that for such observables ‘being above the median’ could be noise sensitive. We shall in this talk present the first progress on Benjamini’s problem, in the context of first-passage percolation. (Joint work with Daniel de la Riva.)