TY - JOUR
T1 - Gaussian unitary ensemble eigenvalues and Riemann [Formula Presented] function zeros
T2 - A nonlinear equation for a new statistic
AU - Forrester, P. J.
AU - Odlyzko, A. M.
PY - 1996
Y1 - 1996
N2 - For infinite Gaussian unitary ensemble random matrices the probability density function [Formula Presented] for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé [Formula Presented] equation. Comparison is made with the empirical value of [Formula Presented] for the zeros of the Riemann [Formula Presented] function on the critical line, including data from [Formula Presented] consecutive zeros near zero number [Formula Presented].
AB - For infinite Gaussian unitary ensemble random matrices the probability density function [Formula Presented] for the nearest neighbor eignenvalue spacing (as distinct from the spacing between consecutive eigenvalues) is computed in terms of the solution of a certain nonlinear equation, which generalizes the σ form of the Painlevé [Formula Presented] equation. Comparison is made with the empirical value of [Formula Presented] for the zeros of the Riemann [Formula Presented] function on the critical line, including data from [Formula Presented] consecutive zeros near zero number [Formula Presented].
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U2 - 10.1103/PhysRevE.54.R4493
DO - 10.1103/PhysRevE.54.R4493
M3 - Article
AN - SCOPUS:0001983595
SN - 1063-651X
VL - 54
SP - R4493-R4495
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 5
ER -