کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772925 | 1631058 | 2018 | 36 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
ترجمه فارسی عنوان
معادلات خاصی از ماتریس های غیر تصادفی و اندازه گیری براون از اپراتورهای غیر معمول: روش کاهش خطی سازی و هرمیتی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
We study the Brown measure of certain non-Hermitian operators arising from Voiculescu's free probability theory. Usually those operators appear as the limit in â-moments of certain ensembles of non-Hermitian random matrices, and the Brown measure gives then a canonical candidate for the limit eigenvalue distribution of the random matrices. A prominent class for our operators is given by polynomials in â-free variables. Other explicit examples include R-diagonal elements and elliptic elements, for which the Brown measure was already known, and a new class of triangular-elliptic elements. Our method for the calculation of the Brown measure is based on a rigorous mathematical treatment of the Hermitian reduction method, as considered in the physical literature, combined with subordination and the linearization trick.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 537, 15 January 2018, Pages 48-83
Journal: Linear Algebra and its Applications - Volume 537, 15 January 2018, Pages 48-83
نویسندگان
Serban T. Belinschi, Piotr Åniady, Roland Speicher,