Noise sensitivity and voronoi percolation

Daniel Ahlberg; Rangel Baldasso

doi:10.1214/18-EJP233

Noise sensitivity and voronoi percolation

Daniel Ahlberg, Rangel Baldasso

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on R². 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.

Original language	English
Article number	108
Journal	Electronic Journal of Probability
Volume	23
DOIs	https://doi.org/10.1214/18-EJP233
State	Published - 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018, University of Washington. All rights reserved.

Funding

The authors thank Augusto Teixeira for valuable discussions. DA thanks Swedish Research Council for financial support through grant 637-2013-7302. RB thanks FAPERJ for financial support through grant E-26/202.231/2015.

Funders	Funder number
Vetenskapsrådet	637-2013-7302
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro	E-26/202.231/2015

Keywords

Conservative perturbations
Noise sensitivity
Voronoi percolation

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AB - In this paper we study noise sensitivity and threshold phenomena for Poisson Voronoi percolation on R2. 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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Noise sensitivity and voronoi percolation

Abstract

Bibliographical note

Funding

Keywords

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