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Eigenvector Convergence for Minors of Unitarily Invariant Infinite Random Matrices
International Mathematics Research Notices ( IF 1.452 ) Pub Date : 2020-01-09 , DOI: 10.1093/imrn/rnz330
Najnudel J.

In [10], Pickrell fully characterizes the unitarily invariant probability measures on infinite Hermitian matrices. An alternative proof of this classification is given by Olshanski and Vershik in [9], and in [3] Borodin and Olshanski deduce from this proof that under any of these invariant measures, the extreme eigenvalues of the minors, divided by the dimension, converge almost surely. In this paper, we prove that one also has a weak convergence for the eigenvectors, in a sense that is made precise. After mapping Hermitian to unitary matrices via the Cayley transform, our result extends a convergence proven in our paper with Maples and Nikeghbali [6], for which a coupling of the circular unitary ensemble of all dimensions is considered.
更新日期:2020-01-09

 

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