Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

Details Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

2010-05-27

arxiv.org/abs/1005.5058v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are compared with known exact results for $\beta=1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.

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