M. Poplavskyi

On the distribution of the largest real eigenvalue for the real Ginibre ensemble

Let $\sqrt{N}+λ_{max}$ be the largest real eigenvalue of a random $N\times N$ matrix with independent $N(0,1)$ entries (the `real Ginibre matrix'). We study the large deviations behaviour of the limiting $N\rightarrow \infty$ distribution $P[λ_{max} 0$, \[ P[λ_{max} 0$ - can be read off from the corresponding answers for $λ_{max}$ using $X_s^{(max)}\stackrel{D}{=} \sqrt{4s}λ_{max}$.