Brunel University Research Archive (BURA) >
Research Areas >
Mathematical Physics >

Please use this identifier to cite or link to this item:

Title: Superstatistical generalisations of Wishart-Laguerre ensembles of random matrices
Authors: Abul-Magd, AY
Akemann, G
Vivo, P
Keywords: Wishart-Laguerre ensembles
Random matrix theory
Publication Date: 2009
Publisher: IOP
Citation: Journal of Physics A: Mathematical and Theoretical. 42: 175207, May 2009
Abstract: Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalized Wishart–Laguerre ensembles of random matrices with Dyson index β = 1, 2 and 4. The entries of the data matrix are Gaussian random variables whose variances η fluctuate from one sample to another according to a certain probability density f(η) and a single deformation parameter γ. Three superstatistical classes for f(η) are usually considered: χ2-, inverse χ2- and log-normal distributions. While the first class, already considered by two of the authors, leads to a power-law decay of the spectral density, we here introduce and solve exactly a superposition of Wishart–Laguerre ensembles with inverse χ2-distribution. The corresponding macroscopic spectral density is given by a γ-deformation of the semi-circle and Marčenko–Pastur laws, on a non-compact support with exponential tails. After discussing in detail the validity of Wigner's surmise in the Wishart–Laguerre class, we introduce a generalized γ-dependent surmise with stretched-exponential tails, which well approximates the individual level spacing distribution in the bulk. The analytical results are in excellent agreement with numerical simulations. To illustrate our findings we compare the χ2- and inverse χ2-classes to empirical data from financial covariance matrices.
Appears in Collections:Mathematics
School of Information Systems, Computing and Mathematics Research Papers
Mathematical Physics

Files in This Item:

File Description SizeFormat
0811.1992v2.pdf431.76 kBAdobe PDFView/Open

Items in BURA are protected by copyright, with all rights reserved, unless otherwise indicated.


Library (c) Brunel University.    Powered By: DSpace
Send us your
Feedback. Last Updated: September 14, 2010.
Managed by:
Hassan Bhuiyan