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Central limit theorems for the brownian motion on large unitary groups

Florent Benaych-Georges (2011)

Bulletin de la Société Mathématique de France

In this paper, we are concerned with the large n limit of the distributions of linear combinations of the entries of a Brownian motion on the group of n × 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 distributions are considered, giving rise to various limit processes, related to the geometric construction of the unitary Brownian motion. As an application, we propose a very short proof of the asymptotic...

Central sequences in the factor associated with Thompson’s group F

Paul Jolissaint (1998)

Annales de l'institut Fourier

We prove that the type II 1 factor L ( F ) generated by the regular representation of F is isomorphic to its tensor product with the hyperfinite type II 1 factor. This implies that the unitary group of L ( F ) is contractible with respect to the topology defined by the natural Hilbertian norm.

Centralizers for subsets of normed algebras

Bertram Yood (2000)

Studia Mathematica

Let G be the set of invertible elements of a normed algebra A with an identity. For some but not all subsets H of G we have the following dichotomy. For x ∈ A either c x c - 1 = x for all c ∈ H or s u p c x c - 1 : c H = . In that case the set of x ∈ A for which the sup is finite is the centralizer of H.

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