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References

  1. C. Aliprantis and K. Border. Infinite Dimensional Analysis: a Hitchhiker's Guide, 2nd ed. (1999) Springer-Verlag. Math. Review 2000k:46001
  2. A. Avez. Entropie des groupes de type fini. C. R. Acad. Sci. Paris Sér. A-B 275 (1972), 1363--1366. Math. Review 0324741
  3. D. Cartwright and B. Krön. Classification of 0-automatic pairs. Preprint (2004).
  4. Y. Derriennic. Quelques applications du théorème ergodique sous-additif. Astérisque 74 (1980), 183-201. Math. Review 82e:60013
  5. Y. Derriennic. Entropie, théorèmes limite et marches aléatoires. Probability measures on groups, VIII (Oberwolfach, 1985) Lecture Notes in Math. 1210 (1986), 241-284, Springer. Math. Review 89f:60076b
  6. E. Dynkin and M. Malyutov. Random walk on groups with a finite number of generators. Sov. Math. Dokl. 2 (1961), 399--402. Math. Review 0131904
  7. D. Epstein, J. Cannon, D. Holt, S. Levy, M. Paterson, and W. Thurston. Word processing in groups. (1992) Jones and Bartlett. Math. Review 93i:20036
  8. H. Furstenberg. Noncommuting random products. Trans. Amer. Math. Soc. 108 (1963), 377-428. Math. Review 0163345
  9. H. Furstenberg. Random walks and discrete subgroups of Lie groups. Advances Probab. Related Topics, Vol. 1 (1971), 1-63, Dekker. Math. Review 0284569
  10. M. Gromov. Hyperbolic groups. Essays in group theory. Math. Sci. Res. Inst. Publ. 8 (1987), 75-263, Springer. Math. Review 89e:20070
  11. Y. Guivarc'h. Sur la loi des grands nombres et le rayon spectral d'une marche aléatoire. Astérisque 74 (1980), 47-98. Math. Review 82g:60016
  12. R. Haring-Smith. Groups and simple languages. Trans. Amer. Math. Soc. 279 (1983), no. 1, 337-356. Math. Review 85b:20045
  13. G. Högnäs and A. Mukherjea. Probability measures on semigroups : convolution products, random walks, and random matrices. The University Series in Mathematics (1995), Plenum Press. Math. Review 97c:60018
  14. V. Kaimanovich. The Poisson formula for groups with hyperbolic properties. Ann. of Math. (2) 152 (2000), no. 3, 659-692. Math. Review 2002d:60064
  15. V. Kaimanovich and A. Vershik. Random walks on discrete groups: boundary and entropy. Ann. Probab. 11 (1983), no. 3, 457-490. Math. Review 85d:60024
  16. J.F.C. Kingman. Subadditive ergodic theory. Ann. Probab. 1 (1973), 883-909. Math. Review 0356192
  17. S. Lalley. Finite range random walk on free groups and homogeneous trees. Ann. Probab. 21 (1993), no. 4, 2087-2130. Math. Review 94m:60051
  18. S. Lalley. Random walks on regular languages and algebraic systems of generating functions. Algebraic methods in statistics and probability. Contemp. Math. 287 (2001), 201-230, Amer. Math. Soc. Math. Review 2002m:60038
  19. F. Ledrappier. Some asymptotic properties of random walks on free groups. Topics in probability and Lie groups: boundary theory. CRM Proc. Lect. Notes 28 (2001), 117-152, Amer. Math. Soc. Math. Review 2002g:60116
  20. R. Lyons. Random walks and the growth of groups. C. R. Acad. Sci., Paris, Sér. I 320 (1995), no. 11, 1361-1366. Math. Review 96e:60015
  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. Mathéus. Random walks on free products of cyclic groups. arXiv:math.PR/0509211 (2005).
  23. J. Mairesse and F. Mathéus. Random walks on groups with a tree-like Cayley graph. Mathematics and computer science. III. Algorithms, trees, combinatorics and probabilities. Trends Math. (2004), 445-460, Birkhäuser. Math. Review 2006a:60076
  24. T. Nagnibeda and W. Woess. Random walks on trees with finitely many cone types. J. Theoret. Probab. 15 (2002), no. 2, 383-422. Math. Review 2003k:60098
  25. S. Sawyer and T. Steger. The rate of escape for anisotropic random walks in a tree. Probab. Theory Related Fields 76 (1987), no. 2, 207-230. Math. Review 89a:60165
  26. P. Soardi. Limit theorems for random walks on discrete semigroups related to nonhomogeneous trees and Chebyshev polynomials. Math. Z. 200 (1989), no. 3, 313-325. Math. Review 90b:60011
  27. J. Stallings. A remark about the description of free products of groups. Proc. Cambridge Philos. Soc. 62 (1966), 129-134. Math. Review 0188332
  28. C. Takacs. Random walk on periodic trees. Electron. J. Probab. 2 (1997), no. 1, 1-16. Math. Review 97m:60101
  29. A. Vershik. Dynamic theory of growth in groups: Entropy, boundaries, examples. Russ. Math. Surv. 55 (2000), no. 4, 667-733. Math. Review 2001m:37019
  30. W. Woess. A description of the Martin boundary for nearest neighbour random walks on free products. Probability measures on groups, VIII (Oberwolfach, 1985) Lecture Notes in Math. 1210 (1986), 203-215, Springer. Math. Review 88i:60121
  31. W. Woess. Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics 138 (2000), Cambridge University Press. Math. Review 2001k:60006


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