Spectral Convergence of Large Block-Hankel Gaussian Random Matrices

Abstract : This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices WN W H N where WN is a M L × N matrix, whose M block lines of dimensions L × N are mutually independent Han-kel matrices constructed from complex Gaussian correlated stationary random sequences. In the asymptotic regime where M → +∞, N → +∞ and M L N → c > 0, it is shown using the Stieltjes transform approach that the empirical eigenvalue distribution of WN W H N has a deterministic behaviour which is characterized.
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Submitted on : Wednesday, October 18, 2017 - 10:00:04 AM
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Philippe Loubaton, Xavier Mestre. Spectral Convergence of Large Block-Hankel Gaussian Random Matrices. Colombo F., Sabadini I., Struppa D., Vajiac M. (eds) Advances in Complex Analysis and Operator Theory. Trends in Mathematics. Birkhäuser, Cham, 2017. ⟨hal-01618531⟩

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