Oded Schramm's contributions to noise sensitivity

TL;DR

This paper surveys Oded Schramm's key contributions to noise sensitivity, including spectral analysis of Boolean functions, shape fluctuations in first passage percolation, and dynamical percolation models.

Contribution

It highlights Schramm's novel work on spectral analysis, shape fluctuations, and dynamical percolation, advancing understanding in these areas.

Findings

Spectral analysis of critical percolation and Boolean functions.

Insights into shape fluctuations in first passage percolation.

Contributions to the theory of dynamical percolation.

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.