Exponential approximation and stein's method of exchangeable pairs

Alea

Volumn 10, Issue 1, 2013, Pages 1-13

  Fulman, Jason ^a   Ross, Nathan ^b  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Exponential approximation; Heat kernel; Random matrix; Stein's method

Indexed keywords

EID: 84877013937     PISSN: 19800436     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. S. Chatterjee, J. Fulman and A. Röllin. Exponential approximation by Stein's method and spectral graph theory. ALEA Lat. Am. J. Probab. Math. Stat. 8, 197-223 (2011). MR2802856.
2. S. Chatterjee and Q. M. Shao. Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model. Ann. Appl. Probab. 21 (2), 464-483 (2011). MR2807964.
3. L. H. Y. Chen, L. Goldstein and Q. M. Shao. Normal approximation by Stein's method. Probability and its Applications (New York). Springer, Heidelberg (2011). MR2732624.
4. M. Coram and P. Diaconis. New tests of the correspondence between unitary eigenvalues and the zeros of Riemann's zeta function. J. Phys. A 36 (12), 2883-2906 (2003). Random matrix theory. MR1986397.
5. P. Diaconis and S. N. Evans. Linear functionals of eigenvalues of random matrices. Trans. Amer. Math. Soc. 353 (7), 2615-2633 (2001). MR1828463.
6. P. Diaconis and M. Shahshahani. On the eigenvalues of random matrices. J. Appl. Probab. 31A, 49-62 (1994). Studies in applied probability. MR1274717.
7. C. Döbler and M. Stolz. Stein's method and the multivariate CLT for traces of powers on the classical compact groups. Electron. J. Probab. 16, no. 86, 2375-2405 (2011). MR2861678.
8. J. Fulman. Stein's method and random character ratios. Trans. Amer. Math. Soc. 360 (7), 3687-3730 (2008). MR2386242.
9. J. Fulman. Stein's method and characters of compact Lie groups. Comm. Math. Phys. 288 (3), 1181-1201 (2009). MR2504870.
10. J. Fulman. Stein's method, heat kernel, and traces of powers of elements of compact lie groups. Electron. J. Probab. 17, no. 66, 1-16 (2012).
11. J. Fulman and A. Röllin. Stein's method, heat kernel, and linear functions on the orthogonal groups. ArXiv Mathematics e-prints (2011). abs/1109.2975v1.
12. A. Grigor'yan. Heat kernel and analysis on manifolds, volume 47 of AMS/IP Stud-ies in Advanced Mathematics. American Mathematical Society, Providence, RI (2009). MR2569498.
13. K. Johansson. On random matrices from the compact classical groups. Ann. of Math. (2) 145 (3), 519-545 (1997). MR1454702.
14. T. Lévy. Schur-Weyl duality and the heat kernel measure on the unitary group. Adv. Math. 218 (2), 537-575 (2008). MR2407946.
15. K. Liu. Heat kernels, symplectic geometry, moduli spaces and finite groups. In Surveys in differential geometry: differential geometry inspired by string theory, volume 5 of Surv. Differ. Geom., pages 527-542. Int. Press, Boston, MA (1999). MR1772278.
16. H. M. Luk. Stein's method for the Gamma distribution and related statistical ap-plications. ProQuest LLC, Ann Arbor, MI (1994). Thesis (Ph.D.)-University of Southern California. MR2693204.
17. E. A. Peköz and A. Röllin. Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chains. Electron. J. Probab. 16, no. 51, 1381-1393 (2011a). MR2827464.
18. E. A. Peköz and A. Röllin. New rates for exponential approximation and the theorems of Rényi and Yaglom. Ann. Probab. 39 (2), 587-608 (2011b). MR2789507.
19. E. M. Rains. Combinatorial properties of Brownian motion on the compact classical groups. J. Theoret. Probab. 10 (3), 659-679 (1997). MR1468398.
20. E. M. Rains. Increasing subsequences and the classical groups. Electron. J. Combin. 5, Research Paper 12, 9 pp. (electronic) (1998). MR1600095.
21. G. Reinert. Three general approaches to Stein's method. In An introduction to Stein's method, volume 4 of Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., pages 183-221. Singapore Univ. Press, Singapore (2005). MR2235451.
22. Y. Rinott and 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 (4), 1080-1105 (1997). MR1484798.
23. Y. Rinott and V. Rotar. Normal approximations by Stein's method. Decis. Econ. Finance 23 (1), 15-29 (2000). MR1780090.
24. S. Rosenberg. The Laplacian on a Riemannian manifold, volume 31 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge (1997). An introduction to analysis on manifolds. MR1462892.
25. N. Ross. Fundamentals of Stein's method. Probab. Surv. 8, 210-293 (2011). MR2861132.
26. C. Stein. Approximate computation of expectations. Institute of Mathematical Statistics Lecture Notes-Monograph Series, 7. Institute of Mathematical Statistics, Hayward, CA (1986). MR882007.