Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the exact orders of critical value in Finitary Random Interlacements   In this paper, we prove the exact orders of critical intensity $u_*(T)$ in
Finitary Random Interlacements (FRI) in $\mathbb{Z}^d, \ d\ge 3$ with respect
to the expected fiber length $T$. We show that as $T\to\infty$,
  $u_*(T)\sim T^{-1}, \ d\ge 5;$
  $u_*(T)\sim T^{-1}\log T, \ d=4;$
  $u_*(T)\sim T^{-1/2},\ d=3.$
  Our estimates also give the order of magnitude at which the percolative phase
transition with respect to $T$ takes place.

35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
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The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol