Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: KPZ equation correlations in time   We consider the narrow wedge solution to the Kardar-Parisi-Zhang stochastic
PDE under the characteristic $3:2:1$ scaling of time, space and fluctuations.
We study the correlation of fluctuations at two different times. We show that
when the times are close to each other, the correlation approaches one at a
power-law rate with exponent $2/3$, while when the two times are remote from
each other, the correlation tends to zero at a power-law rate with exponent
$-1/3$. We also prove exponential-type tail bounds for differences of the
solution at two space-time points.
  Three main tools are pivotal to proving these results: 1) a representation
for the two-time distribution in terms of two independent narrow wedge
solutions; 2) the Brownian Gibbs property of the KPZ line ensemble; and 3)
recently proved one-point tail bounds on the narrow wedge solution.

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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: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an