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arXiv · 1603.05849

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

M. Poplavskyi·Roger Tribe·Oleg Zaboronski
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Abstract

Let $\sqrt{N}+\lambda_{max}$ 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 $P[\lambda_{max} 0$, \[ P[\lambda_{max} 0$ - can be read off from the corresponding answers for $\lambda_{max}$ using $X_s^{(max)}\stackrel{D}{=} \sqrt{4s}\lambda_{max}$.

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BibTeXRIS

M. Poplavskyi, Roger Tribe, Oleg Zaboronski. 2016-03-18. On the distribution of the largest real eigenvalue for the real Ginibre ensemble. https://arxiv.org/abs/1603.05849

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