10,767 research outputs found
Central Limit Theorems for the Brownian motion on large unitary groups
In this paper, we are concerned with the large N limit of linear combinations
of the entries of a Brownian motion on the group of N by N unitary matrices. We
prove that the process of such a linear combination converges to a Gaussian
one. Various scales of time and various initial distribution are concerned,
giving rise to various limit processes, related to the geometric construction
of the unitary Brownian motion. As an application, we propose a quite short
proof of the asymptotic Gaussian feature of the linear combinations of the
entries of Haar distributed random unitary matrices, a result already proved by
Diaconis et al.Comment: 14 page
Album 22: Chinese Students in Europe, 1924-1933 overview
The Album 22 image collection includes 20 loose photographs and miscellaneous items found inside the original album
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