کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4591097 | 1335007 | 2010 | 42 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Central limit theorem for the heat kernel measure on the unitary group
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Central limit theorem for the heat kernel measure on the unitary group Central limit theorem for the heat kernel measure on the unitary group](/preview/png/4591097.png)
چکیده انگلیسی
We prove that for a finite collection of real-valued functions f1,…,fn on the group of complex numbers of modulus 1 which are derivable with Lipschitz continuous derivative, the distribution of under the properly scaled heat kernel measure at a given time on the unitary group U(N) has Gaussian fluctuations as N tends to infinity, with a covariance for which we give a formula and which is of order N−1. In the limit where the time tends to infinity, we prove that this covariance converges to that obtained by P. Diaconis and S.N. Evans in a previous work on uniformly distributed unitary matrices. Finally, we discuss some combinatorial aspects of our results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 259, Issue 12, 15 December 2010, Pages 3163-3204
Journal: Journal of Functional Analysis - Volume 259, Issue 12, 15 December 2010, Pages 3163-3204