Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlation of paths between distinct vertices in a randomly oriented
  graph   We prove that in a random tournament the events $\{s\rightarrow a\}$ and
$\{t\rightarrow b\}$ are positively correlated, for distinct vertices $a,s,b,t
\in K_n.$ It is also proven that the correlation between the events
$\{s\rightarrow a\}$ and $\{t\rightarrow b\}$ in the random graphs $G(n,p)$ and
$G(n,m)$ with random orientation is positive for every fixed $p>0$ and
sufficiently large $n$ (with $m=\left\lfloor p \binom{n}{2}\right\rfloor$). We
conjecture it to be positive for all $p$ and all $n$. An exact recursion for
$\P(\{s\rightarrow a\} \cap \{t\rightarrow b\})$ in $\gnp$ is given.

29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas