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2018 Noise sensitivity and Voronoi percolation
Daniel Ahlberg, Rangel Baldasso
Electron. J. Probab. 23: 1-21 (2018). DOI: 10.1214/18-EJP233


In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on $\mathbb{R} ^2$. In the setting of Boolean functions, both threshold phenomena and noise sensitivity can be understood via the study of randomized algorithms. Together with a simple discretization argument, such techniques apply also to the continuum setting. Via the study of a suitable algorithm we show that box-crossing events in Voronoi percolation are noise sensitive and present a threshold phenomenon with polynomial window. We also study the effect of other kinds of perturbations, and emphasize the fact that the techniques we use apply for a broad range of models.


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Daniel Ahlberg. Rangel Baldasso. "Noise sensitivity and Voronoi percolation." Electron. J. Probab. 23 1 - 21, 2018.


Received: 22 August 2017; Accepted: 8 October 2018; Published: 2018
First available in Project Euclid: 30 October 2018

zbMATH: 06970413
MathSciNet: MR3878133
Digital Object Identifier: 10.1214/18-EJP233

Primary: 60K35
Secondary: 60G55 , 82B43

Keywords: conservative perturbations , Noise sensitivity , Voronoi percolation


Vol.23 • 2018
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