Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Variational Proof of Robust Gaussian Noise Stability   Using the calculus of variations, we prove that a Euclidean set of fixed
Gaussian measure that nearly maximizes Gaussian noise stability is close to a
half space. The main result proves a modification of a conjecture of Eldan from
2013: a robust Borell inequality that removes a logarithmic dependence on the
distance of the set to a half space. For sets of Gaussian measure $1/2$, we
prove Eldan's 2013 conjecture.
  The noise stability of a Euclidean set $A$ with correlation $\rho$ is the
probability that $(X,Y)\in A\times A$, where $X,Y$ are standard Gaussian random
vectors with correlation $\rho\in(-1,1)$.
  Barchiesi, Brancolini and Julin proved that a Euclidean set of fixed Gaussian
measure that nearly minimizes Gaussian surface area is close to a half space,
using a variational "penalty function" method. Our proof adapts their method to
the more general setting of noise stability.
  We also show that half spaces are the only sets that are stable (in the sense
of second variation) for noise stability, generalizing a result of McGonagle
and Ross for Gaussian surface area.

13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph