On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

We consider the deformed Gaussian ensemble \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{n}=H_{n}^{(0)}+M_{n}$\end{document} in which \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{n}^{(0)}$\end{document} is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{n}^{(0)}$\end{document}. Assuming that the Normalized Counting Measure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{n}^{(0)}$\end{document} converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.