Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlation and Relaxation Times for a Stochastic Process with a
  Fat-Tailed Steady-State Distribution   We study a stochastic process defined by the interaction strength for the
return to the mean and a stochastic term proportional to the magnitude of the
variable. Its steady-state distribution is the Inverse Gamma distribution,
whose power-law tail exponent is determined by the ratio of the interaction
strength to stochasticity. Its time-dependence is characterized by a set of
discrete times describing relaxation of respective cumulants to their
steady-state values. We show that as the progressively lower cumulants diverge
with the increase of stochasticity, so do their relaxation times. We
analytically evaluate the correlation function and show that it is determined
by the longest of these times, namely the inverse interaction strength, which
is also the relaxation time of the mean. We also investigate relaxation of the
entire distribution to the steady state and the distribution of relaxations
times, which we argue to be Inverse Gaussian.

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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
2
The categories of this paper are: math
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The categories of this paper are: dg-ga
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg