Wigner surmises and the two-dimensional homogeneous Poisson point process.
We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.
Sakhr
Jamal
J
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Nieminen
John M
JM