The Annals of Probability

Oded Schramm’s contributions to noise sensitivity

Christophe Garban

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We survey in this paper the main contributions of Oded Schramm related to noise sensitivity. We will describe in particular his various works which focused on the “spectral analysis” of critical percolation (and more generally of Boolean functions), his work on the shape-fluctuations of first passage percolation and finally his contributions to the model of dynamical percolation.

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Ann. Probab. Volume 39, Number 5 (2011), 1702-1767.

First available in Project Euclid: 18 October 2011

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Primary: 82C43: Time-dependent percolation [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 42B05: Fourier series and coefficients

Percolation noise sensitivity discrete Fourier analysis hypercontractivity randomized algorithms SLE processes critical exponents first-passage percolation sub-Gaussian fluctuations


Garban, Christophe. Oded Schramm’s contributions to noise sensitivity. Ann. Probab. 39 (2011), no. 5, 1702--1767. doi:10.1214/10-AOP582.

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