16-32 Paul Federbush
Asymptotic Behavior of the Expectation Value of Permanent Products, a Sequel (14K, LaTeX) Apr 12, 16
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. Continuing the computations of the previous paper,, 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  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.''

Files: 16-32.src( 16-32.comments , 16-32.keywords , 82.tex )