The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off


  1. S. Chatterjee, E. Meckes. Multivariate normal approximation using exchangeable pairs. ALEA Lat. Am. J. Probab. Math. Stat. 4 (2008), 257--283. MR2453473 (2010c:60072)
  2. L.H.Y. Chen, Q.M. Shao. Stein's method for normal approximation. An introduction to Stein's method, 1--59, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 4, Singapore Univ. Press, Singapore, 2005. MR2235448
  3. P. Diaconis, M. Shahshahani. On the eigenvalues of random matrices. Studies in applied probability. J. Appl. Probab. 31A (1994), 49--62. MR1274717 (95m:60011)
  4. J. Fulman. Stein's method, heat kernel, and traces of powers of elements of compact Lie groups, 2010. Available on
  5. S. Helgason. Groups and geometric analysis. Integral geometry, invariant differential operators, and spherical functions. Corrected reprint of the 1984 original. Mathematical Surveys and Monographs, 83. American Mathematical Society, Providence, RI, 2000. xxii+667 pp. ISBN: 0-8218-2673-5 MR1790156 (2001h:22001)
  6. C.P. Hughes, Z. Rudnick. Mock-Gaussian behaviour for linear statistics of classical compact groups. Random matrix theory. J. Phys. A 36 (2003), no. 12, 2919--2932. MR1986399 (2004e:60012)
  7. N. Ikeda, S. Watanabe. Stochastic differential equations and diffusion processes. Second edition. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. xvi+555 pp. ISBN: 0-444-87378-3 MR1011252 (90m:60069)
  8. K. Johansson. On random matrices from the compact classical groups. Ann. of Math. (2) 145 (1997), no. 3, 519--545. MR1454702 (98e:60016)
  9. T. LÈvy. Schur-Weyl duality and the heat kernel measure on the unitary group. Adv. Math. 218 (2008), no. 2, 537--575. MR2407946 (2009g:15075)
  10. E. Meckes. On Stein's method for multivariate normal approximation. High dimensional probability V: the Luminy volume, 153--178, Inst. Math. Stat. Collect., 5, Inst. Math. Statist., Beachwood, OH, 2009. MR2797946
  11. L. Pastur, V. Vasilchuk. On the moments of traces of matrices of classical groups. Comm. Math. Phys. 252 (2004), no. 1-3, 149--166. MR2104877 (2005j:60010)
  12. E.M. Rains. Combinatorial properties of Brownian motion on the compact classical groups. J. Theoret. Probab. 10 (1997), no. 3, 659--679. MR1468398 (99f:60016)
  13. Y. Rinott, V. Rotar. On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted U-statistics. Ann. Appl. Probab. 7 (1997), no. 4, 1080--1105. MR1484798 (99g:60050)
  14. G. Reinert, A. R?llin. Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition. Ann. Probab. 37 (2009), no. 6, 2150--2173. MR2573554 (2011e:60047)
  15. E.M. Stein. Topics in harmonic analysis related to the Littlewood-Paley theory. Annals of Mathematics Studies, No. 63 Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo 1970 viii+146 pp. MR0252961 (40 #6176)
  16. C. Stein. A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, pp. 583--602. Univ. California Press, Berkeley, Calif., 1972. MR0402873 (53 #6687)
  17. C. Stein. Approximate computation of expectations. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 7. Institute of Mathematical Statistics, Hayward, CA, 1986. iv+164 pp. ISBN: 0-940600-08-0 MR0882007 (88j:60055)
  18. C. Stein, The accuracy of the normal approximation to the distribution of the traces of powers of random orthogonal matrices. Department of Statistics, Stanford University, Technical Report No. 470, 1995
  19. M. Stolz. On the Diaconis-Shahshahani method in random matrix theory. J. Algebraic Combin. 22 (2005), no. 4, 471--491. MR2191648 (2007i:15036)

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.