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Noise Sensitivity of Percolation via Differential Inequalities by Tassion, Vincent; Vanneuville, Hugo is a scholarly article available to read on EtoBox.

What is Noise Sensitivity of Percolation via Differential Inequalities about?

Consider critical Bernoulli percolation in the plane. We give a new proof of the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary to the previous approaches, we do not use any spectral tool. We rather study differential inequalities satisfied by a dynamical four-arm event, in the spirit of Kesten's proof of scaling relations. We also obtain new results in dynamical percolation. In particular, we prove that the Hausdorff dimension of the set of times with both primal and dual percolation equals $2/3$ a.s.

Author

Tassion, Vincent; Vanneuville, Hugo

Published

2020

Language

EN