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References

  • Avez, André. Limite de quotients pour des marches aléatoires sur des groupes. (French) C. R. Acad. Sci. Paris Sér. A-B 276 (1973), A317--A320. MR0315750
  • Bougerol, Philippe; Jeulin, Thierry. Brownian bridge on hyperbolic spaces and on homogeneous trees. Probab. Theory Related Fields 115 (1999), no. 1, 95--120. MR1715541
  • Cartwright, Donald I. Some examples of random walks on free products of discrete groups. Ann. Mat. Pura Appl. (4) 151 (1988), 1--15. MR0964500
  • Chow, Yuan Shih; Teicher, Henry. Probability theory. Independence, interchangeability, martingales. Third edition. Springer Texts in Statistics. Springer-Verlag, New York, 1997. xxii+488 pp. ISBN: 0-387-98228-0 MR1476912
  • Dekking, F. M. On transience and recurrence of generalized random walks. Z. Wahrsch. Verw. Gebiete 61 (1982), no. 4, 459--465. MR0682573
  • Donsker, M. D.; Varadhan, S. R. S. On the number of distinct sites visited by a random walk. Comm. Pure Appl. Math. 32 (1979), no. 6, 721--747. MR0539157
  • Dvoretzky, A.; Erdös, P. Some problems on random walk in space. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950. pp. 353--367. University of California Press, Berkeley and Los Angeles, 1951. MR0047272
  • Erschler, Anna. Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks. Probab. Theory Related Fields 136 (2006), no. 4, 560--586. MR2257136
  • Feller, William. An introduction to probability theory and its applications. Vol. I. Third edition John Wiley & Sons, Inc., New York-London-Sydney 1968 xviii+509 pp. MR0228020
  • Gerl, Peter. Über die Anzahl der Darstellungen von Worten. (German) Monatsh. Math. 75 (1971), 205--214. MR0295923
  • Gerl, Peter. Diskrete, mittelbare Gruppen. (German) Monatsh. Math. 77 (1973), 307--318. MR0341550
  • Grigorchuk, R. I. Degrees of growth of finitely generated groups and the theory of invariant means. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 48 (1984), no. 5, 939--985. MR0764305
  • Hamana, Yuji. An almost sure invariance principle for the range of random walks. Stochastic Process. Appl. 78 (1998), no. 2, 131--143. MR1657371
  • Hebisch, W.; Saloff-Coste, L. Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. 21 (1993), no. 2, 673--709. MR1217561
  • Jain, Naresh C.; Pruitt, William E. The range of random walk. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. III: Probability theory, pp. 31--50. Univ. California Press, Berkeley, Calif., 1972. MR0410936
  • Kaĭmanovich, V. A.; Vershik, A. M. Random walks on discrete groups: boundary and entropy. Ann. Probab. 11 (1983), no. 3, 457--490. MR0704539
  • Kesten, Harry. Full Banach mean values on countable groups. Math. Scand. 7 1959 146--156. MR0112053
  • Kesten, Harry. Subdiffusive behavior of random walk on a random cluster. Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), no. 4, 425--487. MR0871905
  • Lalley, Steven P. Finite range random walk on free groups and homogeneous trees. Ann. Probab. 21 (1993), no. 4, 2087--2130. MR1245302
  • Levit, B. Ja.; Molčanov, S. A. Invariant chains on a free group with a finite number of generators. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Meh. 26 (1971), no. 4, 80--88. MR0298721
  • R. Lyons and Y. Peres, Probability on Trees and Networks. To appear (2006); see http://mypage.iu.edu/~rdlyons/prbtree/prbtree.html.
  • Nechaev, S. K.; Grosberg, A. Yu.; Vershik, A. M. Random walks on braid groups: Brownian bridges, complexity and statistics. J. Phys. A 29 (1996), no. 10, 2411--2433. MR1396938
  • Paterson, Alan L. T. Amenability. Mathematical Surveys and Monographs, 29. American Mathematical Society, Providence, RI, 1988. xx+452 pp. ISBN: 0-8218-1529-6 MR0961261
  • Pittet, C.; Saloff-Coste, L. On random walks on wreath products. Ann. Probab. 30 (2002), no. 2, 948--977. MR1905862
  • Rudin, Walter. Functional analysis. Second edition. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, 1991. xviii+424 pp. ISBN: 0-07-054236-8 MR1157815
  • Sawyer, Stanley. Isotropic random walks in a tree. Z. Wahrsch. Verw. Gebiete 42 (1978), no. 4, 279--292. MR0491493
  • Sinclair, Alistair. Algorithms for random generation and counting. A Markov chain approach. Progress in Theoretical Computer Science. Birkhäuser Boston, Inc., Boston, MA, 1993. vi+146 pp. ISBN: 0-8176-3658-7 MR1201590
  • Spitzer, Frank. Principles of random walks. Second edition. Graduate Texts in Mathematics, Vol. 34. Springer-Verlag, New York-Heidelberg, 1976. xiii+408 pp. MR0388547
  • Kingman, J. F. C. Subadditive ergodic theory. With discussion by D. L. Burkholder, Daryl Daley, H. Kesten, P. Ney, Frank Spitzer and J. M. Hammersley, and a reply by the author. Ann. Probability 1 (1973), 883--909. MR0356192
  • Vere-Jones, D. Ergodic properties of nonnegative matrices. I. Pacific J. Math. 22 1967 361--386. MR0214145
  • Woess, Wolfgang. Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics, 138. Cambridge University Press, Cambridge, 2000. xii+334 pp. ISBN: 0-521-55292-3 MR1743100
  • Young, Robert. Averaged Dehn functions for nilpotent groups. Topology 47 (2008), no. 5, 351--367. MR2422531


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