Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices
نویسنده
چکیده
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 the 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.
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October 30, 2007 Version 1.2.4 Date 2007-10-30 Title random cluster generation (with specified degree of separation) Author Weiliang Qiu , Harry Joe . Maintainer Weiliang Qiu Depends R (>= 2.0.0), MASS Description The package contains functions for generating random clusters, generating random covariance/correlation matr...
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Description The package contains functions for generating random clusters, generating random co-variance/correlation matrices,calculating a separation index (data and population version) for pairs of clusters or cluster distributions, and 1-D and 2-D projection plots to visualize clusters. The package also contains a function to generate random clusters based on factorial designs with factors s...
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Description The package contains functions for generating random clusters, generating random covariance/correlation matrices, calculating a separation index (data and population version) for pairs of clusters or cluster distributions, and 1-D and 2-D projection plots to visualize clusters. The package also contains a function to generate random clusters based on factorial designs with factors s...
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