Noise sensitivity in continuum percolation
Journal article, 2014

We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first which involves a percolation model with critical probability pc not equal 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures. A quantitative version of this result was recently proved by Keller and Kindler. We give a simple deduction of the non-quantitative result from the unbiased version. We also develop a quite general method of approximating Continuum Percolation models by discrete models with pc bounded away from zero; this method is based on an extremal result on non-uniform hypergraphs.

BOOLEAN FUNCTIONS

VORONOI PERCOLATION

ORTHOGONAL FUNCTIONS

PLANE

Mathematics

SQUARES

DYNAMICAL PERCOLATION

SUM

PRODUCT-SPACES

Author

Daniel Ahlberg

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Erik Broman

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

S. Griffiths

Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro

R. Morris

Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro

Israel Journal of Mathematics

0021-2172 (ISSN)

Vol. 201 2 847-899

Subject Categories

Mathematics

DOI

10.1007/s11856-014-1038-y

More information

Created

10/8/2017