Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evidence of Random Matrix Corrections for the Large Deviations of
  Selberg's Central Limit Theorem   Selberg's central limit theorem states that the values of $\log|\zeta(1/2+i
\tau)|$, where $\tau$ is a uniform random variable on $[T,2T]$, is distributed
like a Gaussian random variable of mean $0$ and standard deviation
$\sqrt{\frac{1}{2}\log \log T}$. It was conjectured by Radziwi{\l}{\l} that
this breaks down for values of order $\log\log T$, where a multiplicative
correction $C_k$ would be present at level $k\log\log T$, $k>0$. This constant
should be equal to the leading asymptotic for the $2k^{th}$ moment of $\zeta$,
as first conjectured by Keating and Snaith using random matrix theory. In this
paper, we provide numerical and theoretical evidence for this conjecture. We
propose that this correction has a significant effect on the distribution of
the maximum of $\log|\zeta|$ in intervals of size $(\log T)^\theta$,
$\theta>0$. The precision of the prediction enables the numerical detection of
$C_k$ even for low $T$'s of order $T=10^8$. A similar correction appears in the
large deviations of the Keating-Snaith central limit theorem for the logarithm
of the characteristic polynomial of a random unitary matrix, as first proved by
F\'eray, M\'eliot and Nikeghbali.

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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol