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. 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. Angel, Omer; Holroyd, Alexander E.; Romik, Dan. Directed random walk on the permutahedron. In preparation.
  3. Angel, Omer; Holroyd, Alexander E.; Romik, Dan; Vir·g, B·lint. Random sorting networks. Adv. Math. 215 (2007), no. 2, 839--868. MR2355610
  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. Berestycki, NathanaÎl. The hyperbolic geometry of random transpositions. Ann. Probab. 34 (2006), no. 2, 429--467. MR2223947 (2007h:60039)
  6. Berestycki, NathanaÎl; Durrett, Rick. A phase transition in the random transposition random walk. Probab. Theory Related Fields 136 (2006), no. 2, 203--233. MR2240787 (2007i:60009)
  7. Bollob·s, BÈla. Random graphs. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London, 1985. xvi+447 pp. ISBN: 0-12-111755-3; 0-12-111756-1 MR0809996 (87f:05152)
  8. Bollob·s, BÈla. The isoperimetric number of random regular graphs. European J. Combin. 9 (1988), no. 3, 241--244. MR0947025 (89e:05180)
  9. Bollob·s, B.; Fernandez de la Vega, W. The diameter of random regular graphs. Combinatorica 2 (1982), no. 2, 125--134. MR0685038 (84c:05075)
  10. Chung, Fan; Lu, Linyuan. The diameter of sparse random graphs. Adv. in Appl. Math. 26 (2001), no. 4, 257--279. MR1826308 (2002c:05138)
  11. 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)
  12. Diaconis, Persi; Graham, R. L. Spearman's footrule as a measure of disarray. J. Roy. Statist. Soc. Ser. B 39 (1977), no. 2, 262--268. MR0652736 (58 #31575)
  13. Diaconis, Persi; Graham, R. L.; Morrison, J. A. Asymptotic analysis of a random walk on a hypercube with many dimensions. Random Structures Algorithms 1 (1990), no. 1, 51--72. MR1068491 (91g:60078)
  14. Diaconis, Persi; Shahshahani, Mehrdad. Generating a random permutation with random transpositions. Z. Wahrsch. Verw. Gebiete 57 (1981), no. 2, 159--179. MR0626813 (82h:60024)
  15. Durrett, Rick. Shuffling chromosomes. J. Theoret. Probab. 16 (2003), no. 3, 725--750. MR2009200 (2004j:92045)
  16. Durrett, Rick. Genome rearrangement. Statistical methods in molecular evolution, 307--323, Stat. Biol. Health, Springer, New York, 2005. MR2161835 (2006f:92021)
  17. Durrett, R.; Neuhauser, C. Particle systems and reaction-diffusion equations. Ann. Probab. 22 (1994), no. 1, 289--333. MR1258879 (95d:60159)
  18. Eriksen, Niklas. Expected number of inversions after a sequence of random adjacent transpositions---an exact expression. Discrete Math. 298 (2005), no. 1-3, 155--168. MR2163446 (2006b:05008)
  19. H. Eriksson, K. Erikkson, and J. Sjostrand Expected number of inversions after k random adjacent transpositions. Formal power series and algebraic combinatorics. Proceedings of the 12th International Conference (FPSAC'00) held in Moscow, June 26--30, 2000. Edited by Daniel Krob, Alexander A. Mikhalev and Alexander V. Mikhalev. Springer-Verlag, Berlin, 2000. xiv+808 pp. ISBN: 3-540-67247-8 MR1798196 (2001f:05002)
  20. Fulman, Jason. Stein's method and descents after riffle shuffles. Electron. J. Probab. 10 (2005), no. 26, 901--924 (electronic). MR2164033 (2007b:60046)
  21. Kendall, David. Rank Correlation Methods, 1970, 4th edn. London: Griffin.
  22. Knuth, Donald. The Art of Computer Programming, Vol. 2. Reading, Mass.: Addison-Wiley.
  23. Saloff-Coste, Laurent. Random Walks on Finite Groups. In: Probability on discrete structures. Edited by Harry Kesten. Encyclopaedia of Mathematical Sciences, 110. Probability Theory, 1. Springer-Verlag, Berlin, 2004. x+351 pp. ISBN: 3-540-00845-4 MR2023649 (2004g:60003)
  24. N.C. Wormald. Models of random regular graphs (survey), 2005. Available at http://www.ms.unimelb.edu.au/$sim$nick/papers/regsurvey.pdf


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