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For parameters $n,\delta,B,C$, we obtained a sharp asymptotic formula for thenumber of $(n+\lfloor n^\delta\rfloor)^2$-dimensional binary contingency tableswith non-uniform margins taking values of $\lfloor BCn\rfloor$ and $\lfloorCn\rfloor$. Furthermore, we compared our sharp asymptotics with the classicalindependence heuristic estimate and proved that the independence heuristicoverestimates by a factor of $e^{\Theta(n^{2\delta})}$. Our comparison is basedon the analysis of the correlation ratio and an explicit bound for the constantin $\Theta$ is also obtained.

Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independence Heuristic