A Few Remarks on the Operator Norm of Random Toeplitz Matrices

We present some results concerning the almost sure behavior of the operator norm of random Toeplitz matrices, including the law of large numbers for the norm, normalized by its expectation (in the i.i.d. case). As tools we present some concentration inequalities for suprema of empirical processes, w...

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Bibliographic Details
Published in:Journal of theoretical probability 2010-03, Vol.23 (1), p.85-108
Main Author: Adamczak, Radosław
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Summary:We present some results concerning the almost sure behavior of the operator norm of random Toeplitz matrices, including the law of large numbers for the norm, normalized by its expectation (in the i.i.d. case). As tools we present some concentration inequalities for suprema of empirical processes, which are refinements of recent results by Einmahl and Li.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-008-0201-7