Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Rigorous Results on the Phase Transition of Finitary Random
  Interlacement   In this paper, we show several rigorous results on the phase transition of
Finitary Random Interlacement (FRI). For the high intensity regime, we show the
existence of a critical fiber length, and give the exact asymptotic of it as
intensity goes to infinity. At the same time, our result for the low intensity
regime proves the global existence of a non-trivial phase transition with
respect to the system intensity.

15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess