کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4590639 | 1334974 | 2013 | 64 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Free convolution operators and free Hall transform
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We define an extension of the polynomial calculus on a Wâ-probability space by introducing an algebra C{Xi:iâI} which contains polynomials. This extension allows us to define transition operators for additive and multiplicative free convolution. It also permits us to characterize the free Segal-Bargmann transform and the free Hall transform introduced by Biane, in a manner which is closer to classical definitions. Finally, we use this extension of polynomial calculus to prove two asymptotic results on random matrices: the convergence for each fixed time, as N tends to â, of the â-distribution of the Brownian motion on the linear group GLN(C) to the â-distribution of a free multiplicative circular Brownian motion, and the convergence of the classical Hall transform on U(N) to the free Hall transform.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 265, Issue 11, 1 December 2013, Pages 2645-2708
Journal: Journal of Functional Analysis - Volume 265, Issue 11, 1 December 2013, Pages 2645-2708
نویسندگان
Guillaume Cébron,