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2022 Norms of randomized circulant matrices
Rafał Lata, Witold Świątkowski
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Electron. J. Probab. 27: 1-23 (2022). DOI: 10.1214/22-EJP799

Abstract

We investigate two-sided bounds for operator norms of random matrices with non-homogenous independent entries. We formulate a lower bound for Rademacher matrices and conjecture that it may be reversed up to a universal constant. We show that our conjecture holds up to loglogn factor for randomized n×n circulant matrices and that the double logarithm may be eliminated under some mild additional assumptions on the coefficients.

Funding Statement

Supported by the National Science Centre, Poland grant 2015/18/A/ST1/00553.

Acknowledgments

The authors would like to thank the anonymous referee for a careful reading of the manuscript and valuable comments.

Citation

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Rafał Lata. Witold Świątkowski. "Norms of randomized circulant matrices." Electron. J. Probab. 27 1 - 23, 2022. https://doi.org/10.1214/22-EJP799

Information

Received: 11 June 2021; Accepted: 18 May 2022; Published: 2022
First available in Project Euclid: 17 June 2022

arXiv: 2106.03139
Digital Object Identifier: 10.1214/22-EJP799

Subjects:
Primary: 60B20
Secondary: 15B20 , 46B09

Keywords: Circulant matrix , non-homogenous random matrix , operator norm

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Vol.27 • 2022
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