Noise sensitivity in continuum percolation
Artikel i vetenskaplig tidskrift, 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

Författare

Daniel Ahlberg

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Erik Broman

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

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

Ämneskategorier

Matematik

DOI

10.1007/s11856-014-1038-y