title: Gaussian point processes and two-by-two random matrix theory.
abstract: The statistics of the multidimensional Gaussian point process are discussed in connection with the spacing statistics of eigenvalues of 2x2 random matrices. We consider the three-dimensional Gaussian point process when two of the coordinates of a point are randomly chosen from a Gaussian distribution having a mean of zero and a variance of sigma;{2}=1 but the third coordinate is chosen from a Gaussian distribution having a variance in the range of 0< or =sigma_{3};{2}< or =1 . The probability density function associated with a random point being at a distance r from the origin is shown to be closely related to the nearest-neighbor spacing distribution of eigenvalues coming from an ensemble of 2x2 matrices defined by the French-Kota-Pandey-Mehta two-matrix model of random matrix theory. An elementary explanation of this result is given.
authors.affiliation: NDI (Northern Digital Inc.), 103 Randall Drive, Waterloo, Ontario, Canada N2V 1C5.
authors.forename: John M
authors.initials: JM
authors.lastname: Nieminen