  We study the random binary contingency tables with non-uniform margin. More
precisely, for parameters $n,\delta,B,C$, we consider $X=(X_{ij})$ with
$X_{ij}\in \lbrace 0,1\rbrace$, the random binary contingency tables whose
first $[n^\delta]$ rows and columns have margin $[BCn]$ and the rest columns
and rows have margin $[Cn]$. We study various asymptotic properties of $X$ as
$n\to \infty$. This answers a question posted by Barvinok.
