Asymptotic Behavior of the Expectation Value of Permanent Products
arXiv:1407.6545
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(perm_m(A) perm_m'(A))) =lim (1/n)ln(E(perm_m(A)))+ +lim (1/n)ln(E(perm_m'(A))) Here the limit is n to infinity, r is fixed, and m and m' are taken as each proportional to n.
8 pages