The Annals of Probability

Oded Schramm’s contributions to noise sensitivity

Christophe Garban

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Abstract

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.

Article information

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

Dates
First available: 18 October 2011

Permanent link to this document
http://projecteuclid.org/euclid.aop/1318940780

Digital Object Identifier
doi:10.1214/10-AOP582

Zentralblatt MATH identifier
05987668

Mathematical Reviews number (MathSciNet)
MR2884872

Subjects
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

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

Citation

Garban, Christophe. Oded Schramm’s contributions to noise sensitivity. The Annals of Probability 39 (2011), no. 5, 1702--1767. doi:10.1214/10-AOP582. http://projecteuclid.org/euclid.aop/1318940780.


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