On transience of card shuffling
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- by Sara Brofferio and Wolfgang Woess PDF
- Proc. Amer. Math. Soc. 129 (2001), 1513-1519 Request permission
Abstract:
We present simple proofs of transience/recurrence for certain card shuffling models, that is, random walks on the infinite symmetric group.References
- D. A. Darling and P. Erdős, On the recurrence of a certain chain, Proc. Amer. Math. Soc. 19 (1968), 336–338. MR 222962, DOI 10.1090/S0002-9939-1968-0222962-X
- Persi Diaconis, Group representations in probability and statistics, Institute of Mathematical Statistics Lecture Notes—Monograph Series, vol. 11, Institute of Mathematical Statistics, Hayward, CA, 1988. MR 964069
- Persi Diaconis and Laurent Saloff-Coste, Comparison techniques for random walk on finite groups, Ann. Probab. 21 (1993), no. 4, 2131–2156. MR 1245303
- Leopold Flatto and Joel Pitt, Recurrence criteria for random walks on countable Abelian groups, Illinois J. Math. 18 (1974), 1–19. MR 341616
- Gregory F. Lawler, Recurrence and transience for a card shuffling model, Combin. Probab. Comput. 4 (1995), no. 2, 133–142. MR 1342857, DOI 10.1017/S096354830000153X
- Terry Lyons, A simple criterion for transience of a reversible Markov chain, Ann. Probab. 11 (1983), no. 2, 393–402. MR 690136
- C. St. J. A. Nash-Williams, Random walk and electric currents in networks, Proc. Cambridge Philos. Soc. 55 (1959), 181–194. MR 124932, DOI 10.1017/s0305004100033879
- Wolfgang Woess, Random walks on infinite graphs and groups—a survey on selected topics, Bull. London Math. Soc. 26 (1994), no. 1, 1–60. MR 1246471, DOI 10.1112/blms/26.1.1
- Maretsugu Yamasaki, Discrete potentials on an infinite network, Mem. Fac. Sci. Shimane Univ. 13 (1979), 31–44. MR 558311
Additional Information
- Sara Brofferio
- Affiliation: Laboratoire de Probabilités, Université de Paris 6, 4 Place Jussieu, 75252 Paris, France
- Email: brofferi@ccr.jussieu.fr
- Wolfgang Woess
- Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano “Bicocca”, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italia
- Address at time of publication: Institut für Mathematik C, Technische Universität Graz, A-8010 Graz, Austria
- Email: woess@weyl.math.tu-graz.ac.at
- Received by editor(s): March 12, 1999
- Received by editor(s) in revised form: July 21, 1999
- Published electronically: October 19, 2000
- Communicated by: Claudia Neuhauser
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1513-1519
- MSC (2000): Primary 60G50, 60J10; Secondary 60B15
- DOI: https://doi.org/10.1090/S0002-9939-00-05632-X
- MathSciNet review: 1709741