# On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble - Mathematical Physics

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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 eigenvaluestatistics in the bulk of the limiting spectrum of $H n$.

Author: ** Tatyana Shcherbyna**

Source: https://arxiv.org/