Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
solv-int
2009-07-11 v3 Spectral Theory
Exactly Solvable and Integrable Systems
Abstract
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions and spacing distributions in terms of them.
Cite
@article{arxiv.solv-int/9804004,
title = {Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices},
author = {Craig A. Tracy and Harold Widom},
journal= {arXiv preprint arXiv:solv-int/9804004},
year = {2009}
}
Comments
22 pages. LaTeX file. Minor correction