Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Percolation probability and critical exponents for site percolation on
  the UIPT   We derive three critical exponents for Bernoulli site percolation on the on
the Uniform Infinite Planar Triangulation (UIPT). First we compute explicitly
the probability that the root cluster is infinite. As a consequence, we show
that the off-critical exponent for site percolation on the UIPT is $\beta =
1/2$. Then we establish an integral formula for the generating function of the
number of vertices in the root cluster. We use this formula to prove that, at
criticality, the probability that the root cluster has at least $n$ vertices
decays like $n^{-1/7}$. Finally, we also derive an expression for the law of
the perimeter of the root cluster and use it to establish that, at criticality,
the probability that the perimeter of the root cluster is equal to $n$ decays
like $n^{-4/3}$. Among these three exponents, only the last one was previously
known. Our main tools are the so-called gasket decomposition of percolation
clusters, generic properties of random Boltzmann maps, as well as analytic
combinatorics.

32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph