Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The distribution of the free path lengths in the periodic
  two-dimensional Lorentz gas in the small-scatterer limit   We study the free path length and the geometric free path length in the model
of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a
complete and rigorous proof for the existence of their distributions in the
small-scatterer limit and explicitly compute them.
  As a corollary one gets a complete proof for the existence of the constant
term $c=2-3\ln 2+\frac{27\zeta(3)}{2\pi^2}$ in the asymptotic formula
$h(T)=-2\ln \eps+c+o(1)$ of the KS entropy of the billiard map in this model,
as conjectured by P. Dahlqvist.

1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom