Document Detail

Spectral density of a Wishart model for nonsymmetric correlation matrices.
MedLine Citation:
PMID:  24266424     Owner:  NLM     Status:  Publisher    
The Wishart model for real symmetric correlation matrices is defined as W=AA^{t}, where matrix A is usually a rectangular Gaussian random matrix and A^{t} is the transpose of A. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically equivalent but different matrices A and B as AB^{t}. The corresponding Wishart model, thus, is defined as C=AB^{t}BA^{t}. We study the spectral density of C for the case when A and B are not statistically independent. The ensemble average of such nonsymmetric matrices, therefore, does not simply vanishes to a null matrix. In this paper we derive a Pastur self-consistent equation which describes spectral density of C at large matrix dimension. We complement our analytic results with numerics.
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Publication Detail:
Type:  JOURNAL ARTICLE     Date:  2013-10-17
Journal Detail:
Title:  Physical review. E, Statistical, nonlinear, and soft matter physics     Volume:  88     ISSN:  1550-2376     ISO Abbreviation:  Phys Rev E Stat Nonlin Soft Matter Phys     Publication Date:  2013 Oct 
Date Detail:
Created Date:  2013-11-25     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  101136452     Medline TA:  Phys Rev E Stat Nonlin Soft Matter Phys     Country:  -    
Other Details:
Languages:  ENG     Pagination:  042130     Citation Subset:  -    
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México.
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