关键词: Gauss酉系综, 相关函数, 矩, Laguerre多项式

Abstract: In the random matrix theory, the 1-level correlation functions R¹_nβ(x) ( β is generally called Dyson's index) can be explained as the distribution density of energy levels which can be found nearby x. As yet, its limit behavior is still remarkably noticed by many mathematicians and physicists. In the case of unitary ensemble (i.e. β=2), the 1-level correlation functions R¹_n2(x) is closely related to the weight function μ(x) in the classical orthogonal polynomial theory. For the simplication of statement, only the Gaussian unitary ensemble case is considered. The authors find that in weak sense, the limit behavior of R¹_n2(x) is not disturbed by appending a "good" nontrivial multiplicative factor to μ(x).

Key words: Gaussian unitary ensembles, correlation functions, moments, laguerre polynomials