On Universality of Bulk Local Regime of the Deformed Laguerre Ensemble
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 $H_n$.
math-ph↗