Spectral Convergence of Large Block-Hankel Gaussian Random Matrices

2017/04/19 by Loubaton, Philippe, Mestre, Xavier
#FOS: Mathematics #Primary 60B20 #Probability (math.PR) #Secondary 15B52

paper · doi:10.48550/arxiv.1704.06651

Abstract

This paper studies the behaviour of the empirical eigenvalue distribution of large random matrices W_N W_N* where W_N is a ML x N matrix, whose M block lines of dimensions L x N are mutually independent Hankel matrices constructed from complex Gaussian correlated stationary random sequences. In the asymptotic regime where M → ∞, N → +∞ and ML/N → c > 0, it is shown using the Stieltjes transform approach that the empirical eigenvalue distribution of W_N W_N* has a deterministic behaviour which is characterized.

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