References & Further Reading
References
- V. A. Marchenko and L. A. Pastur, Distribution of eigenvalues for some sets of random matrices, 1967
Original derivation of the Marchenko-Pastur law.
- Z. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices, Springer, 2nd ed., 2010
Standard reference for Stieltjes transform techniques in RMT.
- D. N. C. Tse and S. V. Hanly, Linear multiuser receivers: Effective interference, effective bandwidth and user capacity, 1999
Introduced effective-interference analysis for large-system CDMA.
- S. Verdú and S. Shamai (Shitz), Spectral efficiency of CDMA with random spreading, 1999
Companion paper deriving spectral efficiency formulas via RMT.
- R. Couillet and M. Debbah, Random Matrix Methods for Wireless Communications, Cambridge University Press, 2011
Comprehensive treatment of deterministic equivalents and free probability for MIMO.
- D. L. Donoho, Neighborly polytopes and sparse solutions of underdetermined linear equations, 2005
Geometric foundation of the Donoho-Tanner phase transition.
- D. L. Donoho and J. Tanner, Observed universality of phase transitions in high-dimensional geometry, 2009
Empirical evidence that the phase transition curve is universal across sensing ensembles.
- D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp, Living on the edge: Phase transitions in convex programs with random data, 2014
Unified treatment of phase transitions via statistical dimension.
- D. V. Voiculescu, K. J. Dykema, and A. Nica, Free Random Variables, American Mathematical Society, 1992
Foundational monograph on free probability.
- J. A. Mingo and R. Speicher, Free Probability and Random Matrices, Springer, 2017
Modern introduction with emphasis on applications.
- A. M. Tulino and S. Verdú, Random Matrix Theory and Wireless Communications, 2004
Early comprehensive survey linking RMT to communications.
- D. L. Donoho, A. Maleki, and A. Montanari, Message-passing algorithms for compressed sensing, 2009
Introduces AMP and shows it saturates the Donoho-Tanner curve.
- R. Couillet, M. Debbah, G. Caire, Deterministic equivalents for the performance analysis of isometric random precoded systems, 2011
Further Reading
Deterministic equivalents for correlated channels
Couillet, Debbah, Silverstein (2011) — large dimensional analysis
Extends the results here to the Kronecker-correlated channel model.
Universality of the phase transition
Bayati-Lelarge-Montanari (2015), Ann. Statist.
Shows the Donoho-Tanner curve is universal across sub-Gaussian ensembles.
Free probability textbook
Nica-Speicher, 'Lectures on the Combinatorics of Free Probability' (2006)
Combinatorial (non-crossing partition) approach to R- and S-transforms.