Eigenvalue results for large scale random Vandermonde matrices with unit complex entries

IEEE Transactions on Information Theory

Volumn 57, Issue 6, 2011, Pages 3938-3954

  Tucci, Gabriel H ^a   Whiting, Philip A ^a  

^a LUCENT TECHNOLOGIES   (United States)

Author keywords

Eigenvalues; limiting distribution; random matrices; Vandermonde matrices

Indexed keywords

EIGEN-VALUE; EIGENVALUE DISTRIBUTIONS; EIGENVALUES; INDEPENDENTLY AND IDENTICALLY DISTRIBUTED; LIMITING DISTRIBUTIONS; MATRIX; RANDOM MATRICES; VANDERMONDE MATRICES; VANDERMONDE MATRIX;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 79957648034     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2137110     Document Type: Article

References (35)

1. Ø. Ryan and M. Debbah, "Asymptotic behaviour of random Vandermonde matrices with entries on the unit circle," IEEE Trans. Inf. Theory, vol. 1, no. 1, pp. 1-27, Jan. 2009.
2. A. Nordio, C. F. Chiasserini, and E. Viterbo, "Reconstruction of multidimensional signals from irregular noisy samples," IEEE Trans. Signal Process., vol. 56, no. 9, pp. 4711-4718, Sep. 2008.
3. N. Alon and J. Spencer, The Probabilistic Method. Hoboken, NJ: Wiley, 1972.
4. T. Anderson, "Asymptotic theory for principal component analysis," Ann. Math. Statist., vol. 34, pp. 122-148, Mar. 1963.
5. B. Porst and B. Friedlander, "Analysis of the relative efficiency of the MUSIC algorithm," IEEE Trans. Acoust. Speech Signal Process., vol. 36, no. 4, pp. 532-544, Apr. 1988. (Pubitemid 18638693)
6. L. Sampaio, M. Kobayashi, Ø. Ryan, and M. Debbah, "Vandermonde matrices for security applications," IEEE Trans. Signal Process., to be published.
7. P. Billingsley, Weak Convergence of Probability Measures. Hoboken, NJ: Wiley, 1968.
8. P. Billingsley, An Introduction to Probability and Measure, 3rd ed. Hoboken, NJ: Wiley, 1995.
9. T. Strohmer, T. Binder, and M. Sussner, "Howto recover smooth object boundaries from noisy medical images," in Proc. IEEE Int. Conf. Image Processing, Lausanne, Switzerland, 1996, pp. 331-334.
10. N. I. Akhiezer, The Classical Moment Problem and Some Related Questions in Analysis. Edinburgh, U.K.: Oliver and Boyd, 1965.
11. L. Moser and M. Wyman, "An asymptotic formula for the bell numbers," Trans. Roy. Soc. Canada, vol. 49, pp. 49-53, 1955.
12. D. C. Champaney, A Handbook of Fourier Theorems. Cambridge, U.K.: Cambridge Univ. Press, 1989.
13. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. New York: Dover, 1965.
14. R. E. Edwards, Fourier Series: A Modern Introduction. Chicago, IL: Holt McDougal, 1967, vol. 1 and 2.
15. W. Feller, An Introduction to Probability Theory and Its Applications. Hoboken, NJ: Wiley, 1957, vol. 1.
16. W. Feller, An Introduction to Probability Theory and Its Applications. Hoboken, NJ: Wiley, 1970, vol. 2.
17. R. A. Horn and C. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1990.
18. L. Harper, "Stirling behavior is asymptotically normal," Ann. Math. Statist., vol. 38, no. 2, pp. 410-414, 1967.
19. A. M. Bruckner, J. Bruckner, and B. Thomson, Real Analysis [Online]. Available: ClassicalRealAnalysis.com 1996
20. E. Telatar, "Capacity of multi-antenna channels," Eur. Trans. Telecoms., vol. 10, pp. 585-595, Nov.-Dec. 1999.
21. H. Krim and M. Viberg, "Two decades of array signal processing research: The parameteric approach," IEEE Signal Process. Mag., vol. 13, no. 4, pp. 67-94, Apr. 1996. (Pubitemid 126518980)
22. R. Norberg, "On the Vandermonde matrix and its application in mathemtical finance," Working Paper No. 162, Laboratory of Actuarial Mathematics, Univ. Copenhagen, Cophenhagen, Denmark, 1999.
23. M. Raab and A. Steger, "Balls Into Bins:ASimple and Tight Analysis," preprint.
24. T. R. Rockafellar, Convex Analysis. Princteon, NJ: Princeton Univ. Press, 1997.
25. E. Seneta, Non-Negative Matrices and Markov Chains. New York: Springer-Verlag, 1981.
26. A. Nica and R. Speicher, Lectures on the Combinatorics of Free Probability. Cambridge, U.K.: Cambridge Univ. Press, 2006.
27. B. Collins, J. A. Mingo, P. Sniady, and R. Speicher, "Second order freeness and fluctuations of random matrices: III higer order freeness and free cumulants," Documenta Math., vol. 12, pp. 1-70, 2007.
28. D. Voiculescu, "Free probability theory," Fields Institute Commun., 1997.
29. D. Voiculescu, K. Dykema, and A. Nica, "Free random variables," CRM Monograph Ser., vol. 1, 1992, AMS.
30. J. H. Wilkinson, The Algebraic Eigenvalue Problem. Oxford, U.K.: Clarendon, 1965.
31. The Online Encyclopedia of Integer Sequences [Online]. Available: http://www.research.att.com/njas/sequences/A001263
32. D. Williams, Probability With Martingales. Cambridge, U.K.: Cambridge Univ. Press, 1991.
33. A. Tulino and S. Verdu, "Random matrix theory and wireless communications," Found. Trends Commun. Theory, 2004.
34. T. Tao, private communication.
35. E. P.Wigner, "Characteristic vectors of bordered matrices with infinite dimensions," Ann. Math., vol. 62, pp. 546-564, 1955.