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

References

  • Biane, Philippe. Free Brownian motion, free stochastic calculus and random matrices. Free probability theory (Waterloo, ON, 1995), 1--19, Fields Inst. Commun., 12, Amer. Math. Soc., Providence, RI, 1997. MR1426833
  • Bump, Daniel; Gamburd, Alex. On the averages of characteristic polynomials from classical groups. Comm. Math. Phys. 265 (2006), no. 1, 227--274. MR2217304
  • Chatterjee, Sourav. Fluctuations of eigenvalues and second order Poincaré inequalities. Probab. Theory Related Fields 143 (2009), no. 1-2, 1--40. MR2449121
  • Collins, Benoît; Stolz, Michael. Borel theorems for random matrices from the classical compact symmetric spaces. Ann. Probab. 36 (2008), no. 3, 876--895. MR2408577
  • Diaconis, Persi; Evans, Steven N. Linear functionals of eigenvalues of random matrices. Trans. Amer. Math. Soc. 353 (2001), no. 7, 2615--2633. MR1828463
  • Diaconis, Persi; Shahshahani, Mehrdad. On the eigenvalues of random matrices. Studies in applied probability. J. Appl. Probab. 31A (1994), 49--62. MR1274717
  • Döbler, Christian; Stolz, Michael. Stein's method and the multivariate CLT for traces of powers on the classical compact groups. Electron. J. Probab. 16 (2011), no. 86, 2375--2405. MR2861678
  • Döbler, C. and Stolz, M., Linear statistics of random matrix eigenvalues via Stein's method, arXiv:1205.5403 (2012).
  • Duits, Maurice; Johansson, Kurt. Powers of large random unitary matrices and Toeplitz determinants. Trans. Amer. Math. Soc. 362 (2010), no. 3, 1169--1187. MR2563725
  • Dumitriu, Ioana; Edelman, Alan. Global spectrum fluctuations for the $\beta$-Hermite and $\beta$-Laguerre ensembles via matrix models. J. Math. Phys. 47 (2006), no. 6, 063302, 36 pp. MR2239975
  • Durrett, Richard. Probability: theory and examples. Second edition. Duxbury Press, Belmont, CA, 1996. xiii+503 pp. ISBN: 0-534-24318-5 MR1609153
  • Fulman, Jason. Stein's method and characters of compact Lie groups. Comm. Math. Phys. 288 (2009), no. 3, 1181--1201. MR2504870
  • Fulman, J. and Röllin, A., Stein's method, heat kernel, and linear functions on the orthogonal groups, arXiv:1109.2975 (2011).
  • Grigor'yan, Alexander. Heat kernel and analysis on manifolds. AMS/IP Studies in Advanced Mathematics, 47. American Mathematical Society, Providence, RI; International Press, Boston, MA, 2009. xviii+482 pp. ISBN: 978-0-8218-4935-4 MR2569498
  • Hughes, C. P.; Rudnick, Z. Mock-Gaussian behaviour for linear statistics of classical compact groups. Random matrix theory. J. Phys. A 36 (2003), no. 12, 2919--2932. MR1986399
  • Johansson, Kurt. On random matrices from the compact classical groups. Ann. of Math. (2) 145 (1997), no. 3, 519--545. MR1454702
  • Jorgenson, Jay; Lang, Serge. The ubiquitous heat kernel. Mathematics unlimited—2001 and beyond, 655--683, Springer, Berlin, 2001. MR1852183
  • Lévy, Thierry. Schur-Weyl duality and the heat kernel measure on the unitary group. Adv. Math. 218 (2008), no. 2, 537--575. MR2407946
  • Liu, Kefeng. Heat kernels, symplectic geometry, moduli spaces and finite groups. Surveys in differential geometry: differential geometry inspired by string theory, 527--542, Surv. Differ. Geom., 5, Int. Press, Boston, MA, 1999. MR1772278
  • Liu, Kefeng. Heat kernel and moduli space. Math. Res. Lett. 3 (1996), no. 6, 743--762. MR1426532
  • Liu, Kefeng. Heat kernel and moduli spaces. II. Math. Res. Lett. 4 (1997), no. 4, 569--588. MR1470427
  • Maher, D., Brownian motion and heat kernels on compact Lie groups and symmetric spaces, Ph.D. thesis, University of New South Wales, 2006.
  • Meckes, Elizabeth. On the approximate normality of eigenfunctions of the Laplacian. Trans. Amer. Math. Soc. 361 (2009), no. 10, 5377--5399. MR2515815
  • Meckes, E., An infinitesimal version of Stein's method of exchangeable pairs, Stanford University Ph.D. thesis, 2006.
  • Pastur, L.; Vasilchuk, V. On the moments of traces of matrices of classical groups. Comm. Math. Phys. 252 (2004), no. 1-3, 149--166. MR2104877
  • Rains, E. M. Combinatorial properties of Brownian motion on the compact classical groups. J. Theoret. Probab. 10 (1997), no. 3, 659--679. MR1468398
  • Rains, E. M. High powers of random elements of compact Lie groups. Probab. Theory Related Fields 107 (1997), no. 2, 219--241. MR1431220
  • Reinert, Gesine. Couplings for normal approximations with Stein's method. Microsurveys in discrete probability (Princeton, NJ, 1997), 193--207, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., 41, Amer. Math. Soc., Providence, RI, 1998. MR1630415
  • Rinott, Yosef; Rotar, Vladimir. Normal approximations by Stein's method. Decis. Econ. Finance 23 (2000), no. 1, 15--29. MR1780090
  • Rinott, Yosef; Rotar, Vladimir. 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
  • Rosenberg, Steven. The Laplacian on a Riemannian manifold. An introduction to analysis on manifolds. London Mathematical Society Student Texts, 31. Cambridge University Press, Cambridge, 1997. x+172 pp. ISBN: 0-521-46300-9; 0-521-46831-0 MR1462892
  • Saloff-Coste, L. Precise estimates on the rate at which certain diffusions tend to equilibrium. Math. Z. 217 (1994), no. 4, 641--677. MR1306030
  • Sarnak, Peter. Arithmetic quantum chaos. The Schur lectures (1992) (Tel Aviv), 183--236, Israel Math. Conf. Proc., 8, Bar-Ilan Univ., Ramat Gan, 1995. MR1321639
  • Sinai, Ya.; Soshnikov, A. Central limit theorem for traces of large random symmetric matrices with independent matrix elements. Bol. Soc. Brasil. Mat. (N.S.) 29 (1998), no. 1, 1--24. MR1620151
  • Soshnikov, Alexander. The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities. Ann. Probab. 28 (2000), no. 3, 1353--1370. MR1797877
  • Stein, C., The accuracy of the normal approximation to the distribution of the traces of powers of random orthogonal matrices. Stanford University Statistics Department technical report no. 470, (1995).
  • Stein, Charles. 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


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