Large Deviations for Random Spectral Measures and Sum Rules
作者： Fabrice Gamboa , Alain Rouault
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摘要: We prove a Large Deviation Principle for the random spec- tral measure associated to pair $(H_N; e)$ where $H_N$ is sampled in GUE(N) and e fixed unit vector (and more generally $\beta$- extension of this model). The rate function consists two parts. contribution absolutely continuous part reversed Kullback information with respect semicircle distribution singular connected extreme eigenvalue GUE. This method also applied Laguerre Jacobi ensembles, but thoses cases expression not so explicit.
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