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

Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/2442

Title: Power-law deformation of wishart-laguerre ensembles of random matrices
Authors: Akemann, G
Vivo, P
Keywords: Matrix models
Financial covariance matrices
Publication Date: 2008
Citation: J. Stat. Mech. (2008) P09002
Abstract: We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index beta=1,2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size NxM for all three beta, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large-N in a certain double scaling limit we obtain a generalised Marcenko-Pastur distribution on the macroscopic scale, and a generalised Bessel-law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power-law tails, where the microscopic limit depends on beta and the difference M-N. In the limit where our parameter governing the power-law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings the generalised Marcenko-Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.
URI: http://fr.arxiv.org/abs/0806.1861
http://bura.brunel.ac.uk/handle/2438/2442
Appears in Collections:Mathematical Physics
Dept of Mathematics Research Papers
Dept of Mathematics Research Papers

Files in This Item:

File Description SizeFormat
AVarXiv1.pdf404.32 kBAdobe PDFView/Open

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