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Noise sensitivity i...
Noise sensitivity in continuum percolation
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- Ahlberg, Daniel, 1982 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematisk statistik,Department of Mathematical Sciences, Mathematical Statistics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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- Broman, Erik, 1977 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematisk statistik,Department of Mathematical Sciences, Mathematical Statistics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology
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- Griffiths, S. (author)
- Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro
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- Morris, R. (author)
- Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro
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(creator_code:org_t)
- 2014-02-07
- 2014
- English.
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In: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 201:2, s. 847-899
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Abstract
Subject headings
Close
- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- DYNAMICAL PERCOLATION
- ORTHOGONAL FUNCTIONS
- VORONOI PERCOLATION
- BOOLEAN FUNCTIONS
- PRODUCT-SPACES
- SQUARES
- PLANE
- SUM
- Mathematics
- BOOLEAN FUNCTIONS
Publication and Content Type
- ref (subject category)
- art (subject category)
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