Top eigenvalue of a random matrix: large deviations and third order phase transition
Satya N. Majumdar 1 Gregory Schehr 1 Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2014, pp.P01012 We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$), unitary ($\beta=2$) […]
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