Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Gaussian Surface Area and Noise Sensitivity of Degree-$d$
  Polynomials   We provide asymptotically sharp bounds for the Gaussian surface area and the
Gaussian noise sensitivity of polynomial threshold functions. In particular we
show that if $f$ is a degree-$d$ polynomial threshold function, then its
Gaussian sensitivity at noise rate $\epsilon$ is less than some quantity
asymptotic to $\frac{d\sqrt{2\epsilon}}{\pi}$ and the Gaussian surface area is
at most $\frac{d}{\sqrt{2\pi}}$. Furthermore these bounds are asymptotically
tight as $\epsilon\to 0$ and $f$ the threshold function of a product of $d$
distinct homogeneous linear functions.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th