Large deviations of the maximum eigenvalue for wishart and Gaussian random matrices.

@article{Majumdar2009LargeDO,
title={Large deviations of the maximum eigenvalue for wishart and Gaussian random matrices.},
author={Satya N. Majumdar and Massimo Vergassola},
journal={Physical review letters},
year={2009},
volume={102 6},
pages={
060601
}
}

We present a Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is general and applies to other related problems, e.g., the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data… CONTINUE READING