Exact results and universal asymptotics in the Laguerre random matrix ensemble

Peter J. Forrester

Type: Article

Publication Date: 1994-05-01

Citations: 67

DOI: https://doi.org/10.1063/1.530883

Abstract

For various values of the parameters in the Laguerre random matrix ensemble, the distribution of the smallest eigenvalue and the scaled n-level distribution function are calculated exactly in terms of generalized hypergeometric functions. In certain cases these functions are expressed as multidimensional integrals, from which asymptotic formulas are calculated and predictions of universal behavior verified.

Locations

Journal of Mathematical Physics - View - PDF

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+	The distribution and moments of the smallest eigenvalue of a random matrix of wishart type	1991	Alan Edelman
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+	Laguerre ensembles of random matrices: Nonuniversal correlation functions	1993	Taro Nagao Keith Slevin
+	Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials	1993	Jyoichi Kaneko
+ PDF Chat	An Asymptotic Expansion for the Noncentral Wishart Distribution	1970	George A. Anderson
+	Commuting differential operators and zonal spherical functions	1987	I. G. Macdonald
+	The spectrum edge of random matrix ensembles	1993	Peter J. Forrester
+	Nonuniversal correlations for random matrix ensembles	1993	Taro Nagao Keith Slevin
+	Some combinatorial properties of Jack symmetric functions	1989	Richard P. Stanley
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