Mixing times of the biased card shuffling and the asymmetric exclusion process

Transactions of the American Mathematical Society

Volumn 357, Issue 8, 2005, Pages 3013-3029

  Benjamini, Itai ^a   Berger, Noam ^b   Hoffman, Christopher ^c   Mossel, Elchanan ^d  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF WASHINGTON   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23244454079     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03610-X     Document Type: Article

References (17)

1. D. Aldons and J. A. Fill, Reversible Markov chains and random walks on graphs, book in preparation, 2002.
2. D. Aldous and P. Diaconis, Shuffling cards and stopping times, Arner. Math. Monthly 93 (1986), no. 5, 333-348. MR0841111 (88a:60021)
3. D. Bayer and P. Diaconis, Trailing the dovetail shuffle to its lair, Annals of Applied Probability 2 (1992), 294-313. MR1161056 (93d:60014)
4. P. Caputo and F. Martinelli, Relaxation time of anisotropic simple exclusion processes and quantum Heisenberg models, Ann. Appl. Probab. 13 (2003), 691-721. MR1972083
5. P. Diaconis, Group representations in probability and statistics, Institute of Mathematical Statistics Lecture Notes - Monograph Series 11 (1988). MR0964069 (90a:60001)
6. P. Diaconis, From shuffling cards to walking around the building: an introduction to modern Markov chain theory, Proceedings of the International Congress of Mathematicians, Vol. I, Berlin, 1998, 187-204. MR1648031 (99e:60154)
7. P. Diaconis and A. Ram, Analysis of systematic scan Metropolis algorithms using Iwahori-Hecke algebra techniques, Michigan Math. J. 48 (2000), 157-190. MR1786485 (2001j:60132)
8. P. Diaconis and L. Saloff-Coste, What do we know about the Metropolis algorithm? 27th Annual STOC, J. Comput. System Sci. 57 (1998), 20-36. MR1649805 (2000b:68094)
9. U. Feige, D. Peleg, P. Raghavan and E. Upfal, Computing with unreliable information, STOC 90 (1990), 128-137.
10. G. Fishman, Coordinate selection rules for Gibbs sampling, Ann. Appl. Probab. 6 (1996), 444-465. MR1398053 (97k:62058)
11. E. Gilbert, Bell Lab technical report, 1955.
12. C. Kipnis, Central limit theorems for infinite series of queues and applications to simple exclusion, Ann. Probab. 14, no. 2, (1986), 397-408. MR0832016 (88a:60173)
13. J. Reeds, unpublished manuscript, 1981.
14. T. M. Liggett, Interacting particle systems, Springer, 1985, Grundlehren der mathematischen Wissenschaften, 276. MR0776231 (86e:60089)
15. T. M. Liggett, Stochastic interacting systems: contact, voter, and exclusion processes, Springer, New York, 1999. Grundlehren der mathematischen Wissenschaften, 324. MR1717346 (2001q:60247)
16. L. Saloff-Coste, Lectures on finite Markov chains, Lectures on probability theory and statistics (Saint-Flour, 1996), 301-413, Lecture Notes in Math., 1665, Springer, 1996. MR1490046 (99b:60119)
17. D. Wilson, Mixing times of lozenge tiling and card shuffling Markov chains, Ann. Appl. Probab. 14, no. 1, (2004), 274-325. MR2023023