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Eigenvalue correlations for generalized Gaussian ensembles

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  • Shukla, Pragya

Abstract

We study the statistical properties of the eigenvalues of a generalized Gaussian ensemble of Hermitian matrices described by a set of the variances of the matrix elements and non-invariant under an unitary transformation. We find that the eigenvalue distribution in this case can be mapped on to the corresponding distribution in Dyson's Brownian ensembles, with a function of variances in the former playing the role of “time” in the latter. The pre-existing information about the spectral correlations of Brownian ensembles can therefore be used to obtain the same for generalized Gaussian ensembles.

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  • Shukla, Pragya, 2000. "Eigenvalue correlations for generalized Gaussian ensembles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 288(1), pages 119-129.
    • Handle: RePEc:eee:phsmap:v:288:y:2000:i:1:p:119-129
    DOI: 10.1016/S0378-4371(00)00418-0
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