STATISTICAL PROPERTIES OF THE EIGENVALUE MOTION OF HERMITIAN MATRICES

It is noted that the t-->infinity distribution for the eigenvalues of the Hermitian matrix H-0 + tV as given by Yukawa [Phys. Lett. A 116 (1986) 227] is identical to a solvable distribution first discussed by Gaudin [Nucl. Phys. 25 (1962) 447]. A new method of calculating the n-particle distribution function is presented. The probability that an interval of length s is free of eigenvalues, which is given exactly by a Fredholm determinant, is analysed in the small and large s limits.