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

  1. Aldous, David; Diaconis, Persi. Shuffling cards and stopping times. Amer. Math. Monthly 93 (1986), no. 5, 333--348. MR0841111 (88a:60021)
  2. Lee, Tzong-Yow; Yau, Horng-Tzer. Logarithmic Sobolev inequality for some models of random walks. Ann. Probab. 26 (1998), no. 4, 1855--1873. MR1675008 (2001b:60090)
  3. Ivona Bezakova and Daniel Stefankovic. Convex combinations of markov chains and sampling linear orderings. In preparation.
  4. Fang Chen, Laszlo Lovasz, and Igor Pak. Lifting markov chains to speed up mixing. In Proceedings of the thirty-first annual ACM symposium on Theory of computing, pages 275--281, New York, NY, USA, 1999. ACM Press. MR1798046
  5. Deepak Dhar. The abelian sandpile and related models. PHYSICA A, 263:4, 1999.
  6. Diaconis, P.; Saloff-Coste, L. Logarithmic Sobolev inequalities for finite Markov chains. Ann. Appl. Probab. 6 (1996), no. 3, 695--750. MR1410112 (97k:60176)
  7. Diaconis, Persi. Group representations in probability and statistics. Institute of Mathematical Statistics Lecture Notes---Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988. vi+198 pp. ISBN: 0-940600-14-5 MR0964069 (90a:60001)
  8. Diaconis, Persi; Saloff-Coste, Laurent. Comparison techniques for random walk on finite groups. Ann. Probab. 21 (1993), no. 4, 2131--2156. MR1245303 (95a:60009)
  9. Diaconis, Persi; Saloff-Coste, Laurent. Comparison theorems for reversible Markov chains. Ann. Appl. Probab. 3 (1993), no. 3, 696--730. MR1233621 (94i:60074)
  10. Diaconis, Persi; Shahshahani, Mehrdad. Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete 57 (1981), no. 2, 159--179. MR0626813 (82h:60024)
  11. Gao, Fuqing; Quastel, Jeremy. Exponential decay of entropy in the random transposition and Bernoulli-Laplace models. Ann. Appl. Probab. 13 (2003), no. 4, 1591--1600. MR2023890 (2005a:60155)
  12. Goel, Sharad. Analysis of top to bottom-$k$ shuffles. Ann. Appl. Probab. 16 (2006), no. 1, 30--55. MR2209335 (Review)
  13. Hoeffding, Wassily. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 1963 13--30. MR0144363 (26 #1908)
  14. Horn, Roger A.; Johnson, Charles R. Topics in matrix analysis. Cambridge University Press, Cambridge, 1991. viii+607 pp. ISBN: 0-521-30587-X MR1091716 (92e:15003)
  15. Miclo, Laurent. Remarques sur l'hypercontractivité et l'évolution de l'entropie pour des chaînes de Markov finies. (French) [Remarks on hypercontractivity and evolution of entropy in finite Markov chains] Séminaire de Probabilités, XXXI, 136--167, Lecture Notes in Math., 1655, Springer, Berlin, 1997. MR1478724 (99b:60104)
  16. Mironov, Ilya. (Not so) random shuffles of RC4. Advances in cryptology---CRYPTO 2002, 304--319, Lecture Notes in Comput. Sci., 2442, Springer, Berlin, 2002. MR2054828 (2004m:94068)
  17. Ravi Montenegro. Duality and evolving set bounds on mixing times.
  18. Ravi Montenegro and Prasad Tetali. Mathematical Aspects of Mixing Times in Markov Chains, volume 1 of Foundations and Trends in Theoretical Computer Science. NOW Publishers, Boston-Delft, 2006.
  19. Elchanan Mossel, Yuval Peres, and Alistair Sinclair. Shuffling by semi-random transpositions. In Proceedings of FOCS 2004, volume 00, pages 572--581, Los Alamitos, CA, USA, 2004. IEEE Computer Society.
  20. Saloff-Coste, Laurent. Random walks on finite groups. Probability on discrete structures, 263--346, Encyclopaedia Math. Sci., 110, Springer, Berlin, 2004. MR2023654 (2004k:60133)
Bookmark and Share


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