On the distribution of the largest real eigenvalue for the real Ginibre ensemble
| Autor: | Oleg Zaboronski, Roger Tribe, Mihail Poplavskyi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
FOS: Physical sciences Fredholm determinant 01 natural sciences Combinatorics Matrix (mathematics) symbols.namesake 60B20 60F10 0103 physical sciences FOS: Mathematics 0101 mathematics 010306 general physics Mathematical Physics Eigenvalues and eigenvectors Brownian motion Mathematics Real Ginibre ensemble Particle system 60B20 Probability (math.PR) High Energy Physics::Phenomenology 010102 general mathematics Mathematical Physics (math-ph) Riemann hypothesis Distribution (mathematics) Scaling limit symbols Statistics Probability and Uncertainty Mathematics - Probability 60F10 |
| Zdroj: | Ann. Appl. Probab. 27, no. 3 (2017), 1395-1413 |
| ISSN: | 1050-5164 |
| Popis: | 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 $X_s^{(max)}\stackrel{D}{=} \sqrt{4s}\lambda_{max}$. Comment: 20 pages, expanded introduction, added references |
| Databáze: | OpenAIRE |
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