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Noise sensitivity in continuum percolation

Daniel Ahlberg (Institutionen för matematiska vetenskaper, matematisk statistik) ; Erik Broman (Institutionen för matematiska vetenskaper, matematisk statistik) ; S. Griffiths ; R. Morris
Israel Journal of Mathematics (0021-2172). Vol. 201 (2014), 2, p. 847-899.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: DYNAMICAL PERCOLATION, ORTHOGONAL FUNCTIONS, VORONOI PERCOLATION, BOOLEAN FUNCTIONS, PRODUCT-SPACES, SQUARES, PLANE, SUM, Mathematics


Pre-print freely available on ArXiv: http://arxiv.org/abs/1108.0310v2



Denna post skapades 2014-11-18. Senast ändrad 2014-12-01.
CPL Pubid: 205983

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur