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arXiv · 0911.2646

On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble

Tatyana Shcherbyna
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Abstract

We consider the deformed Laguerre Ensemble $H_n=\dfrac{1}{m}\Sigma_n^{1/2}A_{m,n}A_{m,n}^*\Sigma_n^{1/2}$ in which $\Sigma_n$ is a positive hermitian matrix (possibly random) and $A_{m,n}$ is a $n\times m$ complex Gaussian random matrix (independent of $\Sigma_n$), $\dfrac{m}{n}\to c>1$. Assuming that the Normalized Counting Measure of $\Sigma_n$ 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 $H_n$.

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Tatyana Shcherbyna. 2009-11-13. On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble. https://arxiv.org/abs/0911.2646

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