Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 for which the critical probability
p_c \ne 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 p_c bounded away from zero; this method is based on an extremal result on
non-uniform hypergraphs.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys