Year: 1995
Type: article
Abstract: 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 $N\ensuremath{\rightarrow}\ensuremath{\infty}$. We prove that $[N(L)\ensuremath{-}〈N(L)〉]/\sqrt{\mathrm{ln}L}$ has a Gaussian distribution when $L\ensuremath{\rightarrow}\ensuremath{\infty}$. 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.
Source: Physical Review Letters
Authors: Ovidiu Costin, Joel L. Lebowitz
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2057524558