Gaussian unitary ensemble
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1: 35.7 Gaussian Hypergeometric Function of Matrix Argument
§35.7 Gaussian Hypergeometric Function of Matrix Argument
►§35.7(i) Definition
… ►Jacobi Form
… ►Confluent Form
… ►Integral Representation
…2: 32.14 Combinatorics
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►The distribution function given by (32.14.2) arises in random matrix theory where it gives the limiting distribution for the normalized largest eigenvalue in the Gaussian Unitary Ensemble of Hermitian matrices; see Tracy and Widom (1994).
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3: Bibliography F
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The Plasma Dispersion Function: The Hilbert Transform of the Gaussian.
Academic Press, London-New York.
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Introduction to the Random Matrix Theory: Gaussian Unitary Ensemble and Beyond.
In Recent Perspectives in Random Matrix Theory and Number Theory,
London Math. Soc. Lecture Note Ser., Vol. 322, pp. 31–78.
4: 4.44 Other Applications
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►For applications of generalized exponentials and generalized logarithms to computer arithmetic see §3.1(iv).
►For an application of the Lambert -function to generalized Gaussian noise see Chapeau-Blondeau and Monir (2002).
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5: 26.21 Tables
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►It also contains a table of Gaussian polynomials up to .
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6: 35.10 Methods of Computation
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►See Yan (1992) for the and functions of matrix argument in the case , and Bingham et al. (1992) for Monte Carlo simulation on applied to a generalization of the integral (35.5.8).
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7: 3.2 Linear Algebra
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§3.2(i) Gaussian Elimination
… ► … ► … ►Iterative Refinement
… ►§3.2(ii) Gaussian Elimination for a Tridiagonal Matrix
…8: 35.9 Applications
§35.9 Applications
…9: 7.1 Special Notation
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►The notations , , and are used in mathematical statistics, where these functions are called the normal or Gaussian probability functions.