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References

  1. Aida, Shigeki; Masuda, Takao; Shigekawa, Ichirō. Logarithmic Sobolev inequalities and exponential integrability. J. Funct. Anal. 126 (1994), no. 1, 83--101. MR1305064 (95m:60111)
  2. Baik, Jinho; Deift, Percy; Johansson, Kurt. On the distribution of the length of the longest increasing subsequence of random permutations. J. Amer. Math. Soc. 12 (1999), no. 4, 1119--1178. MR1682248 (2000e:05006)
  3. Baik, Jinho; Deift, Percy; McLaughlin, Ken T.-R.; Miller, Peter; Zhou, Xin. Optimal tail estimates for directed last passage site percolation with geometric random variables. Adv. Theor. Math. Phys. 5 (2001), no. 6, 1207--1250. MR1926668 (2003h:60141)
  4. Borodin, Alexei; Forrester, Peter J. Increasing subsequences and the hard-to-soft edge transition in matrix ensembles.Random matrix theory. J. Phys. A 36 (2003), no. 12, 2963--2981. MR1986402 (2004m:82060)
  5. Dumitriu, Ioana; Edelman, Alan. Matrix models for beta ensembles. J. Math. Phys. 43 (2002), no. 11, 5830--5847. MR1936554 (2004g:82044)
  6. Edelman, Alan; Sutton, Brian D. From random matrices to stochastic operators. J. Stat. Phys. 127 (2007), no. 6, 1121--1165. MR2331033 (2009b:82037)
  7. El Karoui, N. (2003) On the largest eigenvalue of Wishart matrices with identity covariance when $n$, $p$, and $p/n \rightarrow \infty$. To appear, Bernoulli.
  8. Feldheim, O., Sodin, S. (2009) A universality result for the smallest eigenvalues of certain sample covariance matrices. To appear, Geom. Funct. Anal.
  9. Forrester, P. J. Log-gases and random matrices.London Mathematical Society Monographs Series, 34. Princeton University Press, Princeton, NJ, 2010. xiv+791 pp. ISBN: 978-0-691-12829-0 MR2641363
  10. Forrester, Peter J.; Rains, Eric M. Interrelationships between orthogonal, unitary and symplectic matrix ensembles. Random matrix models and their applications, 171--207, Math. Sci. Res. Inst. Publ., 40, Cambridge Univ. Press, Cambridge, 2001. MR1842786 (2002h:82008)
  11. Johansson, Kurt. Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000), no. 2, 437--476. MR1737991 (2001h:60177)
  12. Johnstone, Iain M. On the distribution of the largest eigenvalue in principal components analysis. Ann. Statist. 29 (2001), no. 2, 295--327. MR1863961 (2002i:62115)
  13. Ledoux, Michel. The concentration of measure phenomenon.Mathematical Surveys and Monographs, 89. American Mathematical Society, Providence, RI, 2001. x+181 pp. ISBN: 0-8218-2864-9 MR1849347 (2003k:28019)
  14. Ledoux, M. Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case. Electron. J. Probab. 9 (2004), no. 7, 177--208 (electronic). MR2041832 (2004m:60070)
  15. Ledoux, M. Deviation inequalities on largest eigenvalues. Geometric aspects of functional analysis, 167--219, Lecture Notes in Math., 1910, Springer, Berlin, 2007. MR2349607 (2009a:60020)
  16. Ledoux, M. A recursion formula for the moments of the Gaussian orthogonal ensemble. Ann. Inst. Henri Poincaré Probab. Stat. 45 (2009), no. 3, 754--769. MR2548502
  17. Qi, Feng. Bounds for the ratio of two gamma functions. J. Inequal. Appl. 2010, Art. ID 493058, 84 pp. MR2611044
  18. Ramírez, José A.; Rider, Brian. Diffusion at the random matrix hard edge. Comm. Math. Phys. 288 (2009), no. 3, 887--906. MR2504858 (2010g:47083)
  19. Ramirez, J., Rider, B., and Virag, B. (2007) Beta ensembles, stochastic Airy spectrum and a diffusion. Preprint, arXiv:math.PR/0607331.
  20. Silverstein, Jack W. The smallest eigenvalue of a large-dimensional Wishart matrix. Ann. Probab. 13 (1985), no. 4, 1364--1368. MR0806232 (87b:60050)
  21. Soshnikov, Alexander. Universality at the edge of the spectrum in Wigner random matrices. Comm. Math. Phys. 207 (1999), no. 3, 697--733. MR1727234 (2001i:82037)
  22. Tao, T., and Vu, V. (2009) Random matrices: Universality of local eigenvalue statistics up to the edge. Preprint, arXiv:0908.1982.
  23. Tracy, Craig A.; Widom, Harold. Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1994), no. 1, 151--174. MR1257246 (95e:82003)
  24. Tracy, Craig A.; Widom, Harold. On orthogonal and symplectic matrix ensembles. Comm. Math. Phys. 177 (1996), no. 3, 727--754. MR1385083 (97a:82055)
  25. Tracy, Craig A.; Widom, Harold. Asymptotics in ASEP with step initial condition. Comm. Math. Phys. 290 (2009), no. 1, 129--154. MR2520510 (2010f:60283)
  26. Trotter, Hale F. Eigenvalue distributions of large Hermitian matrices; Wigner's semicircle law and a theorem of Kac, Murdock, and Szegő. Adv. in Math. 54 (1984), no. 1, 67--82. MR0761763 (86c:60055)
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