Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

Kasper Eriksen; Yang Chen

doi:10.1088/0305-4470/28/6/017

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Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

Kasper Eriksen·Yang Chen

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Abstract

Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized hydrodynamical equation, a universal dependence of the density-density correlator on the external field is found. As an application we obtain a formula for the variance of linear statistics with the parametric dependence exhibited as a Laplace transform.

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Kasper Eriksen, Yang Chen. 1994-10-17. Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble. https://doi.org/10.1088/0305-4470%2F28%2F6%2F017

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