Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical behavior and the limit distribution for long-range oriented
  percolation. II: Spatial correlation   We prove that the Fourier transform of the properly-scaled normalized
two-point function for sufficiently spread-out long-range oriented percolation
with index \alpha>0 converges to e^{-C|k|^{\alpha\wedge2}} for some
C\in(0,\infty) above the upper-critical dimension 2(\alpha\wedge2). This
answers the open question remained in the previous paper [arXiv:math/0703455].
Moreover, we show that the constant C exhibits crossover at \alpha=2, which is
a result of interactions among occupied paths. The proof is based on a new
method of estimating fractional moments for the spatial variable of the
lace-expansion coefficients.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph