Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reaching the best possible rate of convergence to equilibrium for
  solutions of Kac's equation via central limit theorem   Let $f(\cdot,t)$ be the probability density function which represents the
solution of Kac's equation at time $t$, with initial data $f_0$, and let
$g_{\sigma}$ be the Gaussian density with zero mean and variance $\sigma^2$,
$\sigma^2$ being the value of the second moment of $f_0$. This is the first
study which proves that the total variation distance between $f(\cdot,t)$ and
$g_{\sigma}$ goes to zero, as $t\to +\infty$, with an exponential rate equal to
-1/4. In the present paper, this fact is proved on the sole assumption that
$f_0$ has finite fourth moment and its Fourier transform $\varphi_0$ satisfies
$|\varphi_0(\xi)|=o(|\xi|^{-p})$ as $|\xi|\to+\infty$, for some $p>0$. These
hypotheses are definitely weaker than those considered so far in the
state-of-the-art literature, which in any case, obtains less precise rates.

9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph