Random walks on groups and monoids with a markovian harmonic measure

Electronic Journal of Probability

Volumn 10, Issue , 2005, Pages 1417-1441

  Mairesse, Jean ^a  

^a UNIVERSITÉ PARIS DIDEROT   (France)

Author keywords

Finitely generated group or monoid; Free product; Harmonic measure; Random walk

Indexed keywords

EID: 29144441106     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v10-293     Document Type: Article

References (31)

1. C. Aliprantis and K. Border. Infinite Dimensional Analysis: a Hitchhiker’s Guide, 2nd ed. Springer-Verlag, Berlin, 1999.
2. A. Avez. Entropie des groupes de type fini. C. R. Acad. Sci. Paris Sér. A-B, 275:1363-1366, 1972.
3. D. Cartwright and B. Krön. Classification of O-automatic pairs. Preprint, 2004.
4. Y. Derriennic. Quelques applications du theorème ergodique sous-additif. Astérisque, 74:183-201, 1980.
5. Y. Derriennic. Entropie, theorèmes limite et marches aléatoires. In Probability measures on groups, VIII, volume 1210 of Lecture Notes in Math., pages 241-284. Springer, Berlin, 1986.
6. E. Dynkin and M. Malyutov. Random walk on groups with a finite number of generators. Sov. Math. Dokl., 2:399-402, 1961.
7. D. Epstein, J. Cannon, D. Holt, S. Levy, M. Paterson, and W. Thurston. Word processing in groups. Jones and Bartlett, Boston, 1992.
8. H. Furstenberg. Noncommuting random products. Trans. Amer. Math. Soc., 108:377-428, 1963.
9. H. Furstenberg. Random walks and discrete subgroups of Lie groups. In Advances in Probability and Related Topics, Vol. 1, pages 1-63. Dekker, New York, 1971.
10. M. Gromov. Hyperbolic groups. In Essays in group theory, volume 8 of Math. Sci. Res. Inst. Publ., pages 75-263. Springer, 1987.
11. Y. Guivarc’h. Sur la loi des grands nombres et le rayon spectral d’une marche aratoire. Astérisque, 74:47-98, 1980.
12. R. Haring-Smith. Groups and simple languages. Trans. Amer. Math. Soc., 279(1):337-356, 1983.
13. G. Hognâs and A. Mukherjea. Probability measures on semigroups: convolution products, random walks, and random matrices. Plenum, New York, 1995.
14. V. Kaimanovich. The Poisson formula for groups with hyperbolic properties. Ann. of Math. (2), 152(3):659-692, 2000.
15. V. Kaimanovich and A. Vershik. Random walks on discrete groups: boundary and entropy. Ann. Probab., 11(3):457-490, 1983.
16. J. Kingman. Subadditive ergodic theory. Ann. Probab., 1:883-909, 1973.
17. S. Lalley. Finite range random walk on free groups and homogeneous trees. Ann. Probab., 21(4):2087-2130, 1993.
18. S. Lalley. Random walks on regular languages and algebraic systems of generating functions. In Algebraic methods in statistics and probability, volume 287 of Contemp. Math., pages 201-230. Amer. Math. Soc., 2001.
19. F. Ledrappier. Some asymptotic properties of random walks on free groups. In J. Taylor, editor, Topics in probability and Lie groups: boundary theory, number 28 in CRM Proc. Lect. Notes, pages 117-152. American Mathematical Society, 2001.
20. R. Lyons. Random walks and the growth of groups. C. R. Acad. Sci., Paris, Sir. I, 320(11):1361-1366, 1995.
21. J. Mairesse. Zero-automaticity for groups and monoids. Preprint available at http://www.liafa.jussieu.fr/∼mairesse/Article, 2004.
22. J. Mairesse and F. Matheus. Random walks on free products of cyclic groups. arXiv:math.PR/0509211, 2005.
23. J. Mairesse and F. Matheus. Random walks on groups with a tree-like Cayley graph. In Mathematics and computer science. III. Algorithms, trees, combinatorics and probabilities, Trends in Mathematics, pages 445-460. Birkhauser Verlag, 2004.
24. T. Nagnibeda and W. Woess. Random walks on trees with finitely many cone types. J. Theoret. Probab., 15(2):383-422, 2002.
25. S. Sawyer and T. Steger. The rate of escape for anisotropic random walks in a tree. Probab. Theory Related Fields, 76(2):207-230, 1987.
26. P. Soardi. Limit theorems for random walks on discrete semigroups related to nonhomo-geneous trees and Chebyshev polynomials. Math. Z., 200(3):313-325, 1989.
27. J. Stallings. A remark about the description of free products of groups. Proc. Cambridge Philos. Soc., 62:129-134, 1966.
28. C. Takacs. Random walk on periodic trees. Electron. J. Probab., 2:no. 1, 1-16, 1997.
29. A. Vershik. Dynamic theory of growth in groups: Entropy, boundaries, examples. Russ. Math. Surv., 55(4):667-733, 2000. Translation from Usp. Mat. Nauk 55(4):59-128, 2000.
30. W. Woess. A description of the Martin boundary for nearest neighbour random walks on free products. In Probability measures on groups VIII, volume 1210 of Lecture Notes in Math., pages 203-215. Springer, Berlin, 1986.
31. W. Woess. Random walks on infinite graphs and groups. Number 138 in Cambridge Tracts in Mathematics. Cambridge University Press, 2000.