Publication: Strong convergence of eigenangles and eigenvectors for the circular unitary ensemble
Strong convergence of eigenangles and eigenvectors for the circular unitary ensemble
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Maples, K., Najnudel, J., & Nikeghbali, A. (2019). Strong convergence of eigenangles and eigenvectors for the circular unitary ensemble. The Annals of Probability, 47(4), 2417–2458. https://doi.org/10.1214/18-aop1311
Abstract
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Abstract
It is known that a unitary matrix can be decomposed into a product of complex reflections, one for each dimension, and that these reflections are independent and uniformly distributed on the space where they live if the initial matrix is Haar-distributed. If we take an infinite sequence of such reflections, and consider their successive products, then we get an infinite sequence of unitary matrices of increasing dimension, all of them following the circular unitary ensemble. In this coupling, we show that the eigenvalues of the matric
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- Maples, Kenneth
- Najnudel, Joseph
- Nikeghbali, Ashkan
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Citations
Maples, K., Najnudel, J., & Nikeghbali, A. (2019). Strong convergence of eigenangles and eigenvectors for the circular unitary ensemble. The Annals of Probability, 47(4), 2417–2458. https://doi.org/10.1214/18-aop1311
