Paul Federbush
On the Approximate Asymptotic Statistical Independence 
of the Permanents of 0-1 Matrices, I
(21K, latex)

ABSTRACT.  We consider the ensemble of n x n 0 - 1 matrices with all column and row sums 
equal r. We give this ensemble the uniform weighting to construct a measure E. 
We conjecture 
 E(prod_{i=1}^N (perm_{m_i}(A)) = prod_{i=1}^N (E(perm_{m_i}(A)) * (1+ O(1/n^3)) 
In this paper we prove 
 E_1(prod_{i=1}^N (perm_{m_i}(A)) = prod_{i=1}^N (E_1(perm_{m_i}(A)) * (1+ O(1/n^2)) 
and in the sequel paper, number II in this sequence, we show 
 E_1(prod_{i=1}^N (perm_{m_i}(A)) = prod_{i=1}^N (E_1(perm_{m_i}(A)) * (1+ O(1/n^3)) 
where E_1 is the measure constructed on the ensemble of n x n 0 - 1 matrices with 
non-negative integer entries realized as the sum of r random permutation matrices. 
E_1 is often used as an ``approximation'' to E, and the truth of the last equation 
explains why we support the conjecture.