H. Vanneuville & V .Tassion: Noise sensitivity of percolation via differential inequalities

Abstract: Consider planar Bernoulli percolation. In 1999, Benjamini, Kalai and Schramm proved that this model is noise sensitive in a sense that we will recall in the talk. Ten years later, Garban, Pete and Schramm proved sharp noise sensitivity of planar percolation. We present a new proof of this result. Contrary to the previous approaches, we do not use any spectral tool.

In the first part of the talk, Hugo will present the general context as well as some ideas in the case of simplest Boolean functions such as the Iterated Majority function. In the second part of the talk, Vincent will present a sketch of proof based on another point of view, inspired by Kesten’s theory of scaling relations.


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