Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Pet to Split   Various forms of the polynomial ergodic theorem (PET) which attracted
substantial attention in ergodic theory study the limits of expressions having
the form $1/N\sum_{n=1}^NT^{q_1(n)}f_1... T^{q_\ell (n)}f_\ell$ where $T$ is a
weakly mixing measure preserving transformation, $f_i$'s are bounded measurable
functions and $q_i$'s are polynomials taking on integer values on the integers.
Motivated partially by these results we obtain a central limit theorem for
expressions of the form $1/\sqrt{N}\sum_{n=1}^N (X_1(q_1(n))X_2(q_2(n))...
X_\ell(q_\ell(n))-a_1a_2... a_\ell)$ (sum-product limit theorem--SPLIT) where
$X_i$'s are fast $\alpha$-mixing bounded stationary processes, $a_j=EX_j(0)$
and $q_i$'s are positive functions taking on integer values on integers with
some growth conditions which are satisfied, for instance, when $q_i$'s are
polynomials of growing degrees. This result can be applied to the case when
$X_i(n)=T^nf_i$ where $T$ is a mixing subshift of finite type, a hyperbolic
diffeomorphism or an expanding transformation taken with a Gibbs invariant
measure, as well, as to the case when $X_i(n)=f_i(\xi_n)$ where $\xi_n$ is a
Markov chain satisfying the Doeblin condition considered as a stationary
process with respect to its invariant measure.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org