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періодичних видань НАН України
On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble
Репозиторій DSpace/Manakin
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On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble
Посилання:
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.
Підтримка:
The author is grateful to Prof. L. Pastur for many interesting discussions of the problem.
Дата:
2009
Переглядів:
708
Завантажень:
300
Анотація:
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 measure N⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.
