永久产品期望值的渐近性态
Asymptotic Behavior of the Expectation Value of Permanent Products, a Sequel
摘要：
继续文[1]的计算，我们计算了0-1 n × n矩阵系综中两个积和式乘积的期望值的另一种近似，其中行和和与列和相同，且r是一致加权的.在这里，我们考虑伯努利随机矩阵集合，其中每个条目独立地具有概率p=r/n为1，否则为零。我们用E表示[1]的近似系综的期望值，用E* 表示当前近似系综（伯努利随机矩阵系综）的期望值。对于这些lim_{r to infinity}，（lim_{n to infinity}（1/n）ln（E（perm_m（A）- lim_{n to infinity}（1/n）ln（E*（perm_m（A）= 0且lim_{n to infinity}（1/n）ln（E（perm_m（A）perm_m ′（A）= lim_{n to infinity}（1/n）ln（E（perm_m（A）+ lim_{n to infinity}（1/n）ln（E（perm_m '（A）这里和所有这样的公式中，下标m、m'被假定与n成比例。在我们看来，lim_{r to infinity}（lim_{n to infinity}（1/n）ln（E*（perm_m（A）perm_m '（A）- lim_{n to infinity}（1/n）ln（E*（perm_m（A）+ - lim_{n to infinity}（1/n）ln（E*（perm_m'（A）= 0我们相信：“E在这些方程中给了我们”正确“的期望，而E* 只在r到无穷大的极限中是”正确的“。"
英文摘要：
Continuing the computations of the previous paper,[1], we calculate another approximation to the expectation value of the product of two permanents in the ensemble of 0-1 n x n matrices with like row and column sums equal r uniformly weighted. Here we consider the Bernoulli random matrix ensemble where each entry independently has a probability p=r/n of being one, otherwise zero. We denote the expectations of the approximation ensemble of [1] by E, and the expectations of the present approximation ensemble, the Bernoulli random matrix ensemble, by E*. One has for these lim_{r to infinity}( lim_{n to infinity} (1/n) ln(E(perm_m(A))) -lim_{n to infinity} (1/n) ln(E*(perm_m(A))) ) = 0 and lim_{n to infinity} (1/n) ln(E(perm_m(A)perm_m'(A))) = lim_{n to infinity} (1/n) ln(E(perm_m(A))) + lim_{n to infinity} (1/n) ln(E(perm_m'(A))) Here and in all such formulas the subscripts m,m' are assumed proportional to n. It seems likely to us that lim_{r to infinity}( lim_{n to infinity} (1/n) ln(E*(perm_m(A)perm_m'(A))) - lim_{n to infinity} (1/n) ln(E*(perm_m(A))) + - lim_{n to infinity} (1/n) ln(E*(perm_m'(A))) ) = 0 We believe: "E gives us the `correct' expectations in these equations, and E* is only `correct' in the r to infinity limit."
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