The Level Densities of Random Matrix Unitary Ensembles and their Perturbation Invariability

Details The Level Densities of Random Matrix Unitary Ensembles and their Perturbation Invariability The Level Densities of Random Matrix Unitary Ensembles and their Perturbation Invariability

2005-03-10

arxiv.org/abs/math-ph/0503022v1

Physics

Mathematical Physics

20 pages

Scientific paper

Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary ensembles are recovered. At the same time, we study the perturbation invariability of the level densities of random matrix unitary ensembles. After the weight function associated with the 1-level correlation function is appended a polynomial multiplicative factor, the level density is invariant in the weak sense.

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