Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Concentration estimates for the isoperimetric constant of the super
  critical percolation cluster   We consider the Cheeger constant $\phi(n)$ of the giant component of
supercritical bond percolation on $\mathbb{Z}^d/n\mathbb{Z}^d$. We show that
the variance of $\phi(n)$ is bounded by $\frac{\xi}{n^d}$, where $\xi$ is a
positive constant that depends only on the dimension $d$ and the percolation
parameter.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph