Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic representation of fundamental solutions to $\frac{\partial
  u}{\partial t} = \kappa_m \frac{\partial^m u}{\partial x^m}$   For the fundamental solutions of heat-type equations of order $n$ we give a
general stochastic representation in terms of damped oscillations with
generalized gamma distributed parameters. By composing the pseudo-process $X_n$
related to the higher-order heat-type equation with positively skewed stable
r.v.'s $T^j_{1/3}$, $j=1,2, ..., n$ we obtain genuine r.v.'s whose explicit
distribution is given for $n=3$ in terms of Cauchy asymmetric laws. We also
prove that $X_3(T^1_{1/3}(...(T^n_{(1/3)}(t))...))$ has a stable asymmetric
law.

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The categories of this paper are: cs
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The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an