Statistical mechanics of learning multiple orthogonal signals: Asymptotic theory and fluctuation effects

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 1, 2007, Pages

  Hoyle, D C ^a   Rattray, M ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; INFORMATION THEORY; PHASE TRANSITIONS; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL MECHANICS; WIRELESS TELECOMMUNICATION SYSTEMS;

DATA SETS; LEARNING TRANSITION; ORTHOGONAL SIGNALS; SIGNAL DIRECTIONS;

SIGNAL THEORY;

EID: 33846346186     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.016101     Document Type: Article

References (24)

1. A. Engel and C. Van den Broeck, Statistical Mechanics of Learning (Cambridge University Press, Cambridge, 2001).
2. A. M. Tulino and S. Verdu, Random Matrix Theory and Wireless Communication, Vol. 1 of Foundations and Trends in Communication and Information Theory (Now Publishers, Boston, 2004).
3. J. W. Silverstein and P. L. Combettes, IEEE Trans. Signal Process. ITPRED 1053-587X 10.1109/78.149981 40, 2100 (1992).
4. R. Müller, IEEE Trans. Inf. Theory IETTAW 0018-9448 48, 2495 (2002).
5. V. Plerou, P. Gopikrishnan, B. Rosenow, Luis A. Nures Amaral, T. Guhr, and H. E. Stanley, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.066126 65, 066126 (2002).
6. T. L. H. Watkin and J.-P. Nadal, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/6/016 27, 1899 (1994).
7. M. Biehl and A. Mietzner, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/27/6/015 27, 1885 (1994).
8. P. Reimann, C. Van den Broeck, and G. J. Bex, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/29/13/021 29, 3521 (1996).
9. P. Reimann and C. Van den Broeck, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.53.3989 53, 3989 (1996).
10. D. C. Hoyle and M. Rattray, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.026124 69, 026124 (2004).
11. M. Biehl and E. Schlösser, J. Phys. A JPHAC5 0305-4470 31, L97 (1998).
12. E. Schlösser, D. Saad, and M. Biehl, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/32/22/306 32, 4061 (1999).
13. C. Bunzmann, M. Biehl, and R. Urbanczik, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.026117 72, 026117 (2005).
14. I. M. Johnstone, Ann. Stat. ASTSC7 0090-5364 10.1214/aos/1009210543 29, 295 (2001).
15. C. A. Tracy and H. Widom, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF02099545 177, 727 (1996).
16. J. Baik, G. Ben Arous, and S. Péché, Ann. Probab. APBYAE 0091-1798 33, 1643 (2005).
17. R. Urbanczik, Europhys. Lett. EULEEJ 0295-5075 64, 564 (2003).
18. C. Itzykson and J.-M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1989), Vol. 1.
19. D. C. Hoyle and M. Rattray, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2003-00370-1 62, 117 (2003).
20. S. Péché, Ph.D. thesis, Ecole Polytechnique Fédérale de Lausanne (2003).
21. V. A. Marčenko and L. A. Pastur, Math. USSR. Sb. ZZZZZZ 0025-5734 1, 507 (1967).
22. D. Paul (unpublished).
23. J. Baik and J. W. Silverstein J. Multivariate Anal. (to be published).
24. J. R. L. de Almeida and D. Thouless, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/11/5/028 11, 983 (1978).