On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2009
• ISSN: 1812-9471
• Main Author: Shcherbina, T.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106551
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble / T. Shcherbina // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 4. — С. 396-433. — Бібліогр.: 16 назв. — англ.

We consider the deformed Gaussian Ensemble Hn = Hn⁽⁰⁾ +Mn in which Hn⁽⁰⁾ is a hermitian matrix (possibly random) and Mn is the Gaussian Unitary Ensemble (GUE) random matrix (independent of Hn⁽⁰⁾ ). Assuming that the Normalized Counting Measure of Hn⁽⁰⁾converges weakly (in probability) to a nonrandom...