GAUSSIAN FLUCTUATION IN RANDOM MATRICES

被引:162
作者
COSTIN, O
LEBOWITZ, JL
机构
[1] Department of Mathematics and Physics, Rutgers University, New Brunswick
关键词
D O I
10.1103/PhysRevLett.75.69
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Let N(L) be the number of eigenvalues, in an interval of length L, of a matrix chosen at random from the Gaussian orthogonal, unitary, or symplectic ensembles of N by N matrices, in the limit N→. We prove that [N(L)-N(L)]/lnL has a Gaussian distribution when L→. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results on chaotic quantum systems and on the statistics of zeros of the Riemann zeta function. © 1995 The American Physical Society.
引用
收藏
页码:69 / 72
页数:4
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