Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble

Eytan Katzav; Isaac Pérez Castillo

doi:10.1103/PhysRevE.82.040104

Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble

Eytan Katzav^*, Isaac Pérez Castillo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

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 results are compared with known exact results for β=1 finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.

Original language	English
Article number	040104
Journal	Physical Review E
Volume	82
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.82.040104
State	Published - 14 Oct 2010
Externally published	Yes

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abstract = "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 results are compared with known exact results for β=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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Large deviations of the smallest eigenvalue of the Wishart-Laguerre ensemble

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