Noise sensitivity in continuum percolation

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

DYNAMICAL PERCOLATION

ORTHOGONAL FUNCTIONS

VORONOI PERCOLATION

BOOLEAN FUNCTIONS

PRODUCT-SPACES

SQUARES

PLANE

SUM

Mathematics

BOOLEAN FUNCTIONS

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