|
|
|
References
|
|
|
1. |
M. Anttila, K. Ball, I. Perissinaki, “The central limit problem for convex bodies”, Trans. Amer. Math. Soc., 355:12 (2003), 4723–4735 |
2. |
Z. D. Bai, “Convergence rate of expected spectral distributions of large random
matrices. Part I. Wigner matrices”, Ann. Probab., 21 (1993), 625–648 |
3. |
Z. D. Bai, “Methodologies in spectral analysis of large dimensional random matrices:
a review”, Statistica Sinica, 9 (1999), 611–661 |
4. |
R. Bellman, Introduction to matrix analysis, McGraw-Hill Book Company, New York, 1970 |
5. |
S. G. Bobkov, “On concentration of distributions of random weighted sums”, Ann. Probab., 31:1 (2003), 195–215 |
6. |
S. G. Bobkov, “Concentration of distributions of the weighted sums with
Bernoullian coefficients”, Geom. Aspects Funct. Anal., Lect. Notes Math., 1807, 2003, 27–36 |
7. |
S. G. Bobkov, F. Götze, “Exponential integrability and transportation cost related to
logarithmic Sobolev inequalities”, J. Funct. Anal., 163:1 (1999), 1–28 |
8. |
B. V. Bronk, Topics in the theory of random matrices, Thesis, Princeton University, 1964 |
9. |
A. Guionnet, O. Zeitouni, “Concentration of the spectral measure for large matrices”, Electron. Comm. Probab., 5 (2000), 119–136 |
10. |
V. L. Girko, “Asymptotics of the distribution of the spectrum of random matrices”, Russian Math. Surveys, 44 (1989), 3–36 |
11. |
F. Götze, A. N. Tikhomirov, “Rate of convergence to the semi-circular law”, Probab. Theory Relat. Fields, 127 (2003), 228–276 |
12. |
I. S. Gradstein, I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, Inc., New York, 1994 |
13. |
R. Horn, Ch. Johnson, Matrix analysis, Cambridge University Press, New York, 1991 |
14. |
A. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur, “On asymptotic properties of large random matrices with independent
entries”, J. Math. Phys., 37 (1996), 5033–5060 |
15. |
M. Ledoux, “Concentration of measure and logarithmic Sobolev inequalities”, Séminaire de Probabilités, XXXIII, Lect. Notes Math., 1799, 1999, 120–216 |
16. |
M. Ledoux, The concentration of measure phenomenon, Math. Surveys and monographs, 89, AMS, 2001 |
17. |
M. L. Mehta, Random Matrices, 2nd ed., Academic Press, San Diego, 1991 |
18. |
A. Naor, D. Romik, “Projecting the surface measure of the sphere of $\ell_p^n$”, Ann. Inst. H. Poincaré Probab. Statist., 39:2 (2003), 241–261 |
19. |
L. A. Pastur, “Spectra of random self-adjoint operators”, Russian Math. Surveys, 28:1(169) (1973), 3–64 |
20. |
L. A. Pastur, “Eigenvalue distribution of random matrices”, Ann. l'Inst. H. Poincaré, 64 (1996), 325–337 |
21. |
N. Rosenzweig, Statistical mechanics of equally likely quantum systems in
Statistical physics, Brandeis Summer Institute, Vol. 3, Benjamin, New York, 1962 |
22. |
R. M. Salem, A. Zygmund, “Trigonometric series whose terms have random sign”, Acta Math., 91 (1954), 245–301 |
23. |
V. N. Sudakov, “Typical distributions of linear functionals in finite-dimensional
spaces of higher dimension”, Soviet Math. Dokl., 19:6 (1978), 1578–1582 |
24. |
M. Talagrand, “An isoperimetric theorem on the cube and the Kintchine–Kahane
inequalities”, Proc. Amer. Math. Soc., 104:3 (1988), 905–909 |
25. |
H. von Weizsäcker, “Sudakov's typical marginals, random linear functionals, and
a conditional central limit theorem”, Probab. Theory Rel. Fields, 107 (1997), 313–324 |
26. |
E. Wigner, “Characteristic vectors of bordered matrices with infinite dimensions”, Ann. Math., 62 (1955), 548–564 |
27. |
E. Wigner, “On the distribution of the roots of certain symmetric matrices”, Ann. Math., 67 (1958), 325–327 |
28. |
V. M. Zolotarev, “An estimate for the difference between distributions in Lévy metric”, Proceedings of Steklov's Math. Institute, 112, 1971, 224–231 |