Abstract
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.
Citation
Daniel Ahlberg. Rangel Baldasso. "Noise sensitivity and Voronoi percolation." Electron. J. Probab. 23 1 - 21, 2018. https://doi.org/10.1214/18-EJP233
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