کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772397 | 1413366 | 2017 | 33 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Sample variance in free probability
ترجمه فارسی عنوان
واریانس نمونه در احتمال آزاد
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Let X1,X2,â¦,Xn denote i.i.d. centered standard normal random variables, then the law of the sample variance Qn=âi=1n(XiâXâ¾)2 is the Ï2-distribution with nâ1 degrees of freedom. It is an open problem in classical probability to characterize all distributions with this property and in particular, whether it characterizes the normal law. In this paper we present a solution of the free analogue of this question and show that the only distributions, whose free sample variance is distributed according to a free Ï2-distribution, are the semicircle law and more generally so-called odd laws, by which we mean laws with vanishing higher order even cumulants. In the way of proof we derive an explicit formula for the free cumulants of Qn which shows that indeed the odd cumulants do not contribute and which exhibits an interesting connection to the concept of R-cyclicity.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 273, Issue 7, 1 October 2017, Pages 2488-2520
Journal: Journal of Functional Analysis - Volume 273, Issue 7, 1 October 2017, Pages 2488-2520
نویسندگان
Wiktor Ejsmont, Franz Lehner,