Real eigenvalues of elliptic random matrices
| Autor: | Ji Oon Lee, Nam-Gyu Kang, Sung-Soo Byun, Jinyeop Lee |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Polynomial Uniform distribution (continuous) General Mathematics Probability (math.PR) FOS: Physical sciences Mathematical Physics (math-ph) Semicircle law Matrix (mathematics) FOS: Mathematics Representation (mathematics) Random matrix Complex plane Eigenvalues and eigenvectors Mathematics - Probability Mathematical Physics Mathematics |
| Popis: | We consider the real eigenvalues of an $(N \times N)$ real elliptic Ginibre matrix whose entries are correlated through a non-Hermiticity parameter $\tau_N\in [0,1]$. In the almost-Hermitian regime where $1-\tau_N=\Theta(N^{-1})$, we obtain the large-$N$ expansion of the mean and the variance of the number of the real eigenvalues. Furthermore, we derive the limiting empirical distributions of the real eigenvalues, which interpolate the Wigner semicircle law and the uniform distribution, the restriction of the elliptic law on the real axis. Our proofs are based on the skew-orthogonal polynomial representation of the correlation kernel due to Forrester and Nagao. Comment: 27 pages, 3 figures |
| Databáze: | OpenAIRE |
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