Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices
Arnab Sen (University of California, Berkeley)
Abstract
Suppose $s_n$ is the spectral norm of either the Toeplitz or the Hankel matrix whose entries come from an i.i.d. sequence of random variables with positive mean $\mu$ and finite fourth moment. We show that $n^{-1/2}(s_n-n\mu)$ converges to the normal distribution in either case. This behaviour is in contrast to the known result for the Wigner matrices where $s_n-n\mu$ is itself asymptotically normal.
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Pages: 21-27
Publication Date: February 13, 2007
DOI: 10.1214/ECP.v12-1243
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