Multiplicative measures on free groups

International Journal of Algebra and Computation

Volumn 13, Issue 6, 2003, Pages 705-731

  Borovik, Alexandre V ^a   Myasnikov, Alexei G ^b   Remeslennikov, Vladimir N ^c  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b CITY COLLEGE OF NEW YORK   (United States)

^c RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Asymptotic density; Free groups; Generating functions; Growth functions; Measures; Negligible sets; Random walks; Recurrent and amenable groups; Regular sets; Sparse; Thick

Indexed keywords

EID: 0442291619     PISSN: 02181967     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218196703001596     Document Type: Article

References (34)

1. G. N. Arzhantseva, A property of subgroups of infinite index in a free group, Proc. Amer. Math. Soc. 12 (2000), 3205-3210.
2. L. Bartholdi, Counting paths in graphs, Ensign. Math. 45 (1999), 83-131.
3. A. V. Borovik and A. G. Myasnikov, Quotient tests and random walks in computational group theory, in preparation.
4. A. V. Borovik, A. G. Myasnikov and V. N. Remeslennikov, Algorithms for amalgamated products of groups, to appear in Contemporary Math., Amer. Math. Soc.
5. A. V. Borovik, A. G. Myasnikov and V. Shpilrain, Measuring sets in infinite groups, in Computational and Statistical Group Theory, Contemporary Math, Amer. Math. Soc. Providence, RI, 298, pp. 21-42.
6. C. Champetier, Statistical properties of finitely presented groups Adv. Math. 116 (1995), 197-262.
7. N. Chomsky and M. P. Schutzenberger, The algebraic theory of context-free languages, in Computer Programming and Formal Systems, eds. P. Bradford and D. Hirschberg, North-Holland, Amsterdam, 1963, pp. 118-161.
8. J. M. Cohen, Cogrowth and amenability of discrete groups, J. Funct. Anal. 48 (1982), 301-309.
9. M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), 449-457.
10. D. B. A. Epstein, J. W. Cannon, D. F. Holt, S. V. F. Levy, M. S. Paterson and W. P. Thurston, Word Processing in Groups, Jones and Bartlett, Boston, London, 1992.
11. P. Flajolet and R. Sedgwick, Analytic combinatorics: Functional equations, rational and algebraic functions, Res. Rep. INRIA RR4103, January 2001.
12. C. D. Godsil, Algebraic Combinatorics, Chapman and Hall, New York, 1993.
13. R. I. Grigorchuk, Symmetric random walks on discrete groups, Russian Math. Surv. 32 (1977), 217-218.
14. R. I. Grigorchuk, Banach Averages on Homogeneous Spaces and Random Walks, Ph.D. Thesis, Moscow State University, 1978.
15. R. I. Grigorchuk, Invariant measure on homogeneous spaces, Ukrainian Math. J. 31(5) (1978), 490-497.
16. R. I. Grigorchuk, Symmetrical random walks on discrete groups, in Multicomponent Random Systems, eds. R. L. Dobrushin and Ya. G. Sinai, Dekker, New York, 1980, pp. 285-325.
17. M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53-78.
18. G. H. Hardy, Divergent Series, Chelsea, 1991.
19. I. Kapovich and A. G. Myasnikov, Stallings foldings and subgroups of free groups, J. Algebra 248 (2002), 608-668.
20. J. G. Kemeny, J. L. Snell and A. W. Knapp, Denumerable Markov Chains, D. van Nostrand, Princeton, 1966.
21. B. Kitchens, Symbolic Dynamics, Springer, 1998.
22. D. Kouksov, On rationality of the cogrowth series, Proc. Amer. Math. Soc. 126 (1998), 2845-2847.
23. C. F. Miller III, On group-theoretic decision problems and their classification, Ann. Math. Stud., Vol. 68, Princeton University Press, Princeton, NJ, 1971.
24. D. E. Muller and P. E. Schupp, Groups, the theory of ends, and context-free languages, J. Comp. Syst. Sci. 26 (1983), 295-310.
25. A. D. Myasnikov and A. G. Myasnikov, Balanced presentations of the trivial group on two generators and the Andrews-Curtis conjecture, in Groups and Computation III, eds. W. Kantor and A. Seress, de Gruyter, Berlin, 2001, pp. 257-264.
26. Z. Maassarani, Series expansions for lattice Green functions, J. Phys. A: Math. Gen. 33 (2000), 5675-5691.
27. E. W. Montrol, Random walks on lattices, Stochastic processes in mathematical physics and engineering, Proc. Symp. Appl. MAth., Vol. 16 (1964), Amer. Matm. Soc., Providence, RI, pp. 193-220.
28. A. Yu. Ol'shanskii, Almost every group is hyperbolic, Int. J. Algebra Comput. 2 (1992), 1-17.
29. V. J. Rayward-Smith, A First Course in Formal Language Theory, Blackwell Scientific Publications, Oxford, 1983.
30. N. J. A. Sloane, On-line Encyclopedia of Integer Sequences, http://www.research.att.com/̃njas/sequences/Seis.html
31. R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, 1999.
32. G. Quenell, Combinatorics of free product graphs, Contemp. Math. 173 (1994), 257-281.
33. N. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and geometry on groups, in Cambridge Tracts in Mathematics, Vol. 100, Cambridge University Press, Cambridge, 1992.
34. W. Woess, Cogrowth of groups and simple random walks, Arch. Math. 41 (1983), 363-370.