References

1. Aldous, David . Random walks on finite groups and rapidly mixing Markov chains. Seminar on probability, XVII, 243--297, Lecture Notes in Math., 986, Springer, Berlin, 1983. MR0770418 (86j:60156)
2. Aldous, David ; Diaconis, Persi . Shuffling cards and stopping times. Amer. Math. Monthly 93 (1986), no. 5, 333--348. MR0841111 (88a:60021)
3. Aldous, David ; Diaconis, Persi . Strong uniform times and finite random walks. Adv. in Appl. Math. 8 (1987), no. 1, 69--97. MR0876954 (88d:60175)
4. Bayer, Dave ; Diaconis, Persi . Trailing the dovetail shuffle to its lair. Ann. Appl. Probab. 2 (1992), no. 2, 294--313. MR1161056 (93d:60014)
5. Brown, Mark ; Shao, Y.-S. Identifying coefficients in the spectral representation for first passage time distribution. Probab. Engrg. Inform. Sci, 1(1):69--74, 1987. Math. Review number not available.
6. Chen, Guan-Yu. The cut-off phenomenon for finite Markov chains. PhD thesis, Cornell University, 2006.
7. Chen, Guan-Yu ; Saloff-Coste, Laurent. The cut-off phenomenon for randomized riffle shuffles. To appear in Random Structures Algorithms.
8. Diaconis, Persi. Group representations in probability and statistics. Institute of Mathematical Statistics Lecture Notes---Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988. MR0964069 (90a:60001)
9. Diaconis., Persi . The cutoff phenomenon in finite Markov chains. Proc. Nat. Acad. Sci. U.S.A., 93(4):1659--1664, 1996. MR1374011(97b:60112)
10. Diaconis, Persi ; Fill, James Allen ; Pitman, Jim . Analysis of top to random shuffles. Combin. Probab. Comput. 1 (1992), no. 2, 135--155. MR1179244 (93f:60011)
11. Diaconis, Persi ; Saloff-Coste, Laurent . Comparison techniques for random walk on finite groups. Ann. Probab. 21 (1993), no. 4, 2131--2156. MR1245303 (95a:60009)
12. Diaconis, Persi ; Saloff-Coste, Laurent . Separation cut-offs for birth and death chains. Ann. Appl. Probab. 16 (2006), no. 4, 2098--2122. MR2288715
13. Diaconis, Persi ; Shahshahani, Mehrdad . Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete 57 (1981), no. 2, 159--179. MR0626813 (82h:60024)
14. Dunford, Nelson ; Schwartz, Jacob. T. Linear operators. Part I. Wiley Classics Library. John Wiley & Sons Inc., New York, 1988. MR1009162 (90g:47001a)
15. Feller, William . An introduction to probability theory and its applications. Vol. I. Third edition. John Wiley & Sons Inc., New York, 1968. MR0228020 (37 #3604)
16. Ismail, Mourad E. H. ; Masson, David R. ; Letessier, Jean ; Valent, Galliano . Birth and death processes and orthogonal polynomials. Orthogonal polynomials (Columbus, OH, 1989), 229--255, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht, 1990. MR1100296 (93c:42021)
17. Karlin, Samuel ; McGregor, James . Ehrenfest urn models. J. Appl. Probability 2 1965 352--376. MR0184284 (32 #1757)
18. Karlin, Samuel ; McGregor, James L. The Hahn polynomials, formulas and an application. Scripta Math. 26 1961 33--46. MR0138806 (25 #2249)
19. Keilson, Julian . Markov chain models---rarity and exponentiality. Applied Mathematical Sciences, 28. Springer-Verlag, New York-Berlin, 1979. xiii+184 pp. ISBN: 0-387-90405-0 MR0528293 (80f:60061)
20. Miclo, L. An example of application of discrete Hardy's inequalities. Markov Process. Related Fields 5 (1999), no. 3, 319--330. MR1710983 (2000h:60081)
21. Peres, Yuval ; Revelle, David . Mixing times for random walks on finite lamplighter groups. Electron. J. Probab. 9 (2004), no. 26, 825--845 (electronic). MR2110019 (2005m:60007)
22. Porod, Ursula . The cut-off phenomenon for random reflections. Ann. Probab. 24 (1996), no. 1, 74--96. MR1387627 (97e:60012)
23. Porod, U. The cut-off phenomenon for random reflections. II. Complex and quaternionic cases. Probab. Theory Related Fields 104 (1996), no. 2, 181--209. MR1373375 (97e:60013)
24. Rosenthal, Jeffrey S. Random rotations: characters and random walks on ${rm SO}(N)$. Ann. Probab. 22 (1994), no. 1, 398--423. MR1258882 (95c:60008)
25. Saloff-Coste, Laurent. Convergence to equilibrium and logarithmic Sobolev constant on manifolds with Ricci curvature bounded below. Colloq. Math. 67 (1994), no. 1, 109--121. MR1292948 (95g:58258)
26. Saloff-Coste, L. Precise estimates on the rate at which certain diffusions tend to equilibrium. Math. Z. 217 (1994), no. 4, 641--677. MR1306030 (95m:60115)
27. Saloff-Coste, L. On the convergence to equilibrium of Brownian motion on compact simple Lie groups. J. Geom. Anal. 14 (2004), no. 4, 715--733. MR2111426 (2005m:58081)
28. Saloff-Coste, Laurent . Lectures on finite Markov chains. Lectures on probability theory and statistics (Saint-Flour, 1996), 301--413, Lecture Notes in Math., 1665, Springer, Berlin, 1997. MR1490046 (99b:60119)
29. Saloff-Coste, Laurent . Random walks on finite groups. Probability on discrete structures, 263--346, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. MR2023654 (2004k:60133)
30. Saloff-Coste, Laurent ; Woess, Wolfgang . Transition operators on co-compact $G$-spaces. Rev. Mat. Iberoamericana 22 (2006), no. 3, 747--799. MR2320401
31. Van Assche, W. ; Parthasarathy, P. R. ; Lenin, R. B. Spectral representation of four finite birth and death processes. Math. Sci. 24 (1999), no. 2, 105--112. MR1746330 (2001c:60140)