Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Limit theorems in the stadium billiard   We prove that the Birkhoff sums for ``almost every'' relevant observable in
the stadium billiard obey a non-standard limit law. More precisely, the usual
central limit theorem holds for an observable if and only if its integral along
a one-codimensional invariant set vanishes, otherwise a $\sqrt{n\log n}$
normalization is needed. As one of the two key steps in the argument, we obtain
a limit theorem that holds in Young towers with exponential return time
statistics in general, an abstract result that seems to be applicable to many
other situations.

4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc