Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The existence phase transition for two Poisson random fractal models   In this paper we study the existence phase transition of the random fractal
ball model and the random fractal box model. We show that both of these are in
the empty phase at the critical point of this phase transition.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom