Asymptotic Behavior of the Expectation Value of Permanent Products
Abstract
We would desire to have done the calculations of this paper in the measure on nxn matrices that weights uniformly all 0-1 matrices with row and column sum equal to r, other matrices given weight zero. Instead we work with all matrices that are the sum of r independent uniformly weighted permutation matrices, with the hope that the computations we perform give the same result in this measure. We derive the result for limiting expectations lim (1/n)ln(E(permm(A) permm'(A))) =lim (1/n)ln(E(permm(A)))+ +lim (1/n)ln(E(permm'(A))) Here the limit is n to infinity, r is fixed, and m and m' are taken as each proportional to n.
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