Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Potential Distribution on Random Electrical Networks   Let $G=(V,E)$ be a random electronic network with the boundary vertices which
is obtained by assigning a resistance of each edge in a random graph in
$\mathbb{G}(n,p)$ and the voltages on the boundary vertices. In this paper, we
prove that the potential distribution of all vertices of $G$ except for the
boundary vertices are very close to a constant with high probability for
$p=\frac{c\ln n}{n}$ and $c>1$.

6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg