Limit theorems for permanents. (English. Ukrainian original) Zbl 0941.60019

Girko, V. L.

Theory Probab. Math. Stat. 53, 33-42 (1996); translation from Teor. Jmovirn. Mat. Stat. 53, 29-38 (1995).

A limit theorem is proved for permanents of matrices with positive elements as the order of matrices tends to infinity. As a corollary the invariance principle for the twice stochastic matrices is obtained. The key idea is to use the analytic relation between the permanent and the determinant of the random matrix with uncorrelated elements. The knowledge of the asymptotic behaviour of permanents of matrices is very useful in the calculation of permanents of matrices of higher order.

Reviewer: O.G.Kukush (Kyïv)

MSC:

60B99	Probability theory on algebraic and topological structures
60F99	Limit theorems in probability theory

Keywords:

permanent; random matrix; limit theorem