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arXiv 0911.2646math-phmath.MP
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关于变形Laguerre环系的体局域态的普适性

On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble

Tatyana Shcherbyna

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27 pages, 3 figures
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摘要：

考虑变形拉盖尔包络$H_n=\dfrac{1}{m}Σ_n^{1/2}A_{m,n}A_{m,n}^*Σ_n^{1/2}$，其中$Σ_n$是正厄米矩阵（可能是随机的），$A_{m,n}$是$n\times m$复高斯随机矩阵（与$Σ_n$无关），$\dfrac{m}{n}\to c>1$ .假设$Σ_n$的归一化计数测度以概率弱收敛到具有有界支撑的非随机测度$N^{(0)}$，我们证明了局部特征值统计量在$H_n$的极限谱中的普遍性.

英文摘要：

We consider the deformed Laguerre Ensemble $H_n=\dfrac{1}{m}Σ_n^{1/2}A_{m,n}A_{m,n}^*Σ_n^{1/2}$ in which $Σ_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a $n\times m$ complex Gaussian random matrix (independent of $Σ_n$), $\dfrac{m}{n}\to c>1$. Assuming that the Normalized Counting Measure of $Σ_n$ converges weakly (in probability) to a non-random measure $N^{(0)}$ with a bounded support we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of $H_n$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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