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High Dimensional Probability VI pp 247–260Cite as

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On the Operator Norm of Random Rectangular Toeplitz Matrices

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Part of the book series: Progress in Probability ((PRPR,volume 66))

Abstract

We consider rectangular N x n Toeplitz matrices generated by sequences of centered independent random variables and provide bounds on their operator norm under the assumption of finiteness of pth moments (p > 2). We also show that if N ≫ n log n then with high probability such matrices preserve the Euclidean norm up to an arbitrarily small error.

Mathematics Subject Classification (2010). 60B20, 60E15.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL-02-097, Warszawa, Poland

    Radosław Adamczak

Authors
  1. Radosław Adamczak
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Correspondence to Radosław Adamczak .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology, Atlanta, 30332, USA

    Christian Houdré

  2. University of Delaware, Newark, 19716, USA

    David M. Mason

  3. University of Tennessee, Knoxville, 37934, USA

    Jan Rosiński

  4. University of Washington, Seattle, 98195, USA

    Jon A. Wellner

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Adamczak, R. (2013). On the Operator Norm of Random Rectangular Toeplitz Matrices. In: Houdré, C., Mason, D., Rosiński, J., Wellner, J. (eds) High Dimensional Probability VI. Progress in Probability, vol 66. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0490-5_16

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