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Asymptotic, Global Theory of Random Matrices

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Abstract

The chapter contains standard results for asymptotic, global theory of random matrices. The goal is for readers to compare these results with results of non-asymptotic, local theory of random matrices (Chap. 5. A recent treatment of this subject is given by Qiu et al. [5].

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Notes

  1. 1.

    The foundational preference is a meta-mathematical one rather than a mathematical one.

  2. 2.

    This is only possible because of the highly non-commutative nature of these matrices; this is not possible for non-trivial commuting independent random variables to be freely independent.

  3. 3.

    This table is primarily compiled from [390].

Bibliography

  1. R. Qiu, Z. Hu, H. Li, and M. Wicks, Cognitiv Communications and Networking: Theory and Practice. John Wiley and Sons, 2012.

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  2. T. Tao, Topics in Random Matrix Thoery. American Mathematical Society, 2012.

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  3. T. Tao, Topics in Random Matrix Theory. Amer Mathematical Society, 2012.

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  4. D. Voiculescu, “Limit laws for random matrices and free products,” Inventiones mathematicae, vol. 104, no. 1, pp. 201–220, 1991.

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  5. Ø. Ryan, A. Masucci, S. Yang, and M. Debbah, “Finite dimensional statistical inference,” Information Theory, IEEE Transactions on, vol. 57, no. 4, pp. 2457–2473, 2011.

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  6. R. Couillet and M. Debbah, Random Matrix Methods for Wireless Communications. Cambridge University Press, 2011.

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  7. A. Tulino and S. Verdu, Random matrix theory and wireless communications. now Publishers Inc., 2004.

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  8. R. Müller, “Applications of large random matrices in communications engineering,” in Proc. Int. Conf. on Advances Internet, Process., Syst., Interdisciplinary Research (IPSI), Sveti Stefan, Montenegro, 2003.

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Author information

Authors and Affiliations

  1. Tennessee Technological University, Cookeville, Tennessee, USA

    Robert Qiu

  2. Utica, NY, USA

    Michael Wicks

Authors
  1. Robert Qiu
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  2. Michael Wicks
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Qiu, R., Wicks, M. (2014). Asymptotic, Global Theory of Random Matrices. In: Cognitive Networked Sensing and Big Data. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4544-9_6

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  • DOI: https://doi.org/10.1007/978-1-4614-4544-9_6

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4543-2

  • Online ISBN: 978-1-4614-4544-9

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