Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thin-shell concentration for random vectors in Orlicz balls via moderate
  deviations and Gibbs measures   In this paper, we study the asymptotic thin-shell width concentration for
random vectors uniformly distributed in Orlicz balls. We provide both
asymptotic upper and lower bounds on the probability of such a random vector
$X_n$ being in a thin shell of radius $\sqrt{n}$ times the asymptotic value of
$n^{-1/2}\left(\mathbb E\left[\| X_n\|_2^2\right]\right)^{1/2}$ (as
$n\to\infty$), showing that in certain ranges our estimates are optimal. In
particular, our estimates significantly improve upon the currently best known
general Lee-Vempala bound when the deviation parameter $t=t_n$ goes down to
zero as the dimension $n$ of the ambient space increases. We shall also
determine in this work the precise asymptotic value of the isotropic constant
for Orlicz balls. Our approach is based on moderate deviation principles and a
connection between the uniform distribution on Orlicz balls and Gibbs measures
at certain critical inverse temperatures with potentials given by Orlicz
functions, an idea recently presented by Kabluchko and Prochno in [The maximum
entropy principle and volumetric properties of Orlicz balls, J. Math. Anal.
Appl. {\bf 495}(1) 2021, 1--19].

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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph