Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A central limit theorem for reversible processes with non-linear growth
  of variance   Kipnis and Varadhan showed that for an additive functional, $S_n$ say, of a
reversible Markov chain the condition $E(S_n^{2})/n \to \kappa \in (0,\infty)$
implies the convergence of the conditional distribution of
$S_n/\sqrt{E(S_n^{2}})$, given the starting point, to the standard normal
distribution. We revisit this question under the weaker condition, $E(S_n^{2})
= n\ell(n)$, where $\ell$ is a slowly varying function. It is shown by example
that the conditional distribution of $S_n/\sqrt{E(S_n^{2}})$ need not converge
to the standard normal distribution in this case; and sufficient conditions for
convergence to a (possibly non-standard) normal distribution are developed.

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
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat