Large deviations and phase transitions in spectral linear statistics of Gaussian random matrices

Alexander Valov, Baruch Meerson, Pavel V. Sasorov

We evaluate, in the large-$N$ limit, the complete probability distribution $\mathcal{P}(A,m)$ of the values $A$ of the sum ${\sum }_{i=1}^N|{\lambda }_i{|}^m$, where ${\lambda }_i$ ($i=1,2,\dots ,N$)…