Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Evolution equations of the probabilistic generalization of the Voigt
  profile function   The spectrum profile that emerges in molecular spectroscopy and atmospheric
radiative transfer as the combined effect of Doppler and pressure broadenings
is known as the Voigt profile function. Because of its convolution integral
representation, the Voigt profile can be interpreted as the probability density
function of the sum of two independent random variables with Gaussian density
(due to the Doppler effect) and Lorentzian density (due to the pressure
effect). Since these densities belong to the class of symmetric L\'evy stable
distributions, a probabilistic generalization is proposed as the convolution of
two arbitrary symmetric L\'evy densities. We study the case when the widths of
the considered distributions depend on a scale-factor $\tau$ that is
representative of spatial inhomogeneity or temporal non-stationarity. The
evolution equations for this probabilistic generalization of the Voigt function
are here introduced and interpreted as generalized diffusion equations
containing two Riesz space-fractional derivatives, thus classified as
space-fractional diffusion equations of double order.

8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph