Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central limit theorem for a class of one-dimensional kinetic equations   We introduce a class of Boltzmann equations on the real line, which
constitute extensions of the classical Kac caricature. The collisional gain
operators are defined by smoothing transformations with quite general
properties. By establishing a connection to the central limit problem, we are
able to prove long-time convergence of the equation's solutions towards a limit
distribution. If the initial condition for the Boltzmann equation belongs to
the domain of normal attraction of a certain stable law $g_\alpha$, then the
limit is non-trivial and is a statistical mixture of dilations of $g_\alpha$.
Under some additional assumptions, explicit exponential rates for the
equilibration in Wasserstein metrics are calculated, and strong convergence of
the probability densities is shown.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga