Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

Details Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

1994-10-17

arxiv.org/abs/cond-mat/9410050v1

J. Phys. A>. Math. Gen. 28 (1995) 1627

Physics

Condensed Matter

23 pages, latex

Scientific paper

10.1088/0305-4470/28/6/017

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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