Spectral norm of random large dimensional noncentral Toeplitz and Hankel matrices
Arup Bose, Indian Statistical Institute
Arnab Sen, University of California, Berkeley
Abstract
Suppose sn 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 μ and finite fourth moment. We show that
n-1/2(sn-nμ) converges to the normal distribution in either case. This
behaviour is in contrast to the known result for the Wigner matrices where
sn-nμ is itself asymptotically normal.
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