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Quantitative Version of a Silverstein’s Result

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Geometric Aspects of Functional Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2116))

Abstract

We prove a quantitative version of a Silverstein’s Theorem on the 4-th moment condition for convergence in probability of the norm of a random matrix. More precisely, we show that for a random matrix with i.i.d. entries, satisfying certain natural conditions, its norm cannot be small.

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Acknowledgements

We are grateful to A. Pajor for useful comments and to S. Sodin for bringing reference [5] to our attention. Research partially supported by the E.W.R. Steacie Memorial Fellowship.

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Authors and Affiliations

  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada, T6G 2G1

    Alexander E. Litvak & Susanna Spektor

Authors
  1. Alexander E. Litvak
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  2. Susanna Spektor
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Correspondence to Alexander E. Litvak .

Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Bo'az Klartag

  2. Technion - Israel Institute of Technology, Haifa, Israel

    Emanuel Milman

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Litvak, A.E., Spektor, S. (2014). Quantitative Version of a Silverstein’s Result. In: Klartag, B., Milman, E. (eds) Geometric Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 2116. Springer, Cham. https://doi.org/10.1007/978-3-319-09477-9_21

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