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References

  1. Barlow, M.T. (1995) Diffusion on Fractals, Lectures on Probability Theory and Statistics, Ecole dété  de Probabilités de Saint-Flour XXV - 1995, Lecture Notes Math. 1690, Springer,1998, 1-121 Math. Review 2000a:60148
  2. Barlow, M.T. and Bass, R.F. (1989)The Construction of the Brownian Motion on the Sierpinski Carpet, Ann. Inst. H. Poincaré, 25, (1989) 225-257 Math. Review 91d:60183
  3. Barlow, M.T. and Bass, R.F. (1999) Random walks on graphical Sierpinski carpets, In Random walks and discrete potential theory, ed. M. Picardello, W. Woess, CUP 1999. Math. Review number not available
  4. Barlow, M.T., Coulhon, T. and Grigor'yan (2000) Manifolds and graphs with slow heat kernel decay, to appear in Invenciones Math. Math. Review number not available
  5. Barlow, M.T. and Hambly, B. (1997) Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets, Ann. I. H. Poincaré,33,1997, 531-559 Math. Review 98k:60137
  6. Boukricha, A. (1979)Das Picard-Prinzip und verwandte Fragen bei StH{o}rung von harmonischen Raumen, Math. Ann.,239,1979,247-270 Math. Review 91h:31018
  7. Coulhon, T. (1997)Analysis on infinite graphs with regular volume growth, JE 2070, No 17/18, November 1997, Université de Cergy-Pontoise Math. Review number not available
  8. Coulhon, T. and Grigor'yan, A. (1998) Random walks on graphs with regular volume growth, Geometry and Functional Analysis, 1998, 8, 656-701 Math. Review 99e:60153
  9. Delmotte, T. (1999) Parabolic Harnack inequality and estimates of Markov chains on graphs, Revista Matemática Iberoamericana, 15,(1999),181-232 Math. Review 2000b:35103
  10. Doyle, P.G. and Snell, J.L. (1984) Random walks and electric networks, Carus Mathematical Monographs, 22,Math. Assoc. of Amer., Washington, D.C., 1984 Math. Review number not available
  11. Fabes, E. and Stroock, D. (1986) A new proof of the Moser's parabolic Harnack inequality using the old ideas of Nash, Arch. Rat., Mech. Anal. 96, 1986,327-338 Math. Review 88b:35037
  12. Grigor'yan, A. (1994)Heat kernel upper bounds on a complete non-compact Riemannian manifold, Revista Matemática Iberoamericana, 10,1994,395-452 Math. Review 96b:58107
  13. Grigor'yan, A. (1997) Gaussian upper bounds for the heat kernel on arbitrary manifolds, J. Differential Geometry, 45,1997, 33-5 Math. Review 98g:58167
  14. Grigor'yan, A. (1999) Analytic and geometric background of recurrence and non-explosion of the Brownian motion on the Riemannian manifolds,Bulletin (new ser.) of the American Mathematical Society, S 0273-0979, (1999),00776-4 Math. Review 99k:58195
  15. Grigor'yan, A. (2000) Isoperimetric inequalities and capacities on Riemannian manifolds. The Maz'ya anniversary collection Vol. 1. (Rostock 1998.) 139-157, Oper. Theory Adv. Appl., 109 Birkhauser Basel 1999. Math. Review number not available
  16. Grigor'yan, A. and Telcs, A. (2000) Sub-Gaussian estimates of heat kernels on infinite graphs, to appera in Duke Math. J. Math. Review number not available
  17. Hebish, W. and Saloff-Coste L. (2000) On the relation between elliptic and parabolic Harnack inequalities, preprint Math. Review number not available
  18. Kemeny, J.G., Snell, J.L., Knapp, A.W., (1976) Denumerable Markov Chains, Springer 1976 Math. Review 53#11748
  19. Moser, J.,(1961) On Harnack's theorem for elliptic differential equations, Communications of Pure and Applied Mathematics, 14,1961,577-591 Math. Review 28#2356
  20. Moser, J., (1964) On Harnack's Theorem for parabolic differential equations, Communications of Pure and Applied Mathematics, 17,1964,101-134 Math. Review 28#2357
  21. Nash-Williams, C. St.,J.A., (1959) Random walks and electric current in networks, Proc. Camb. Phil. Soc., 55,(1959),181-194 Math. Review number not available
  22. Pittet, Ch., Saloff-Coste, L., (2000) A survey on the relationship between volume growth, isoperimetry, and the behavior of simple random walk on Cayley graphs, with samples, preprint Math. Review number not available
  23. Saloff-Coste, L., (1992) A note on Poincaré, Sobolev and Harnack inequalities, Duke Mathematical J. IMRN, 2,1992, 27-38 Math. Review number not available
  24. Saloff-Coste, L., (1995) Isoperimetric Inequalities and decay of iterated kernels for almost-transitive Markov chains, Combinatorics, Probability and Computing,4, (1995),419-442 Math. Review number not available
  25. Telcs, A., (1989) Random Walks on Graphs, Electric Networks and Fractals, J. Prob. Theo. and Rel. Fields, (1989), 82, 435-449 Math. Review 90h:60065
  26. Telcs, A.,(1990) Spectra of Graphs and Fractal Dimensions I., . Prob. Theo. and Rel. Fields, (1990), 85, 489-497 Math. Review 91k:60075
  27. Telcs, A.,(1995) Spectra of graphs and Fractal dimensions II, J. Theor. Prob. (1995), 8, 77-96 Math. Review 96d:60107
  28. Telcs, A.,(2000) Fractal Dimension and Martin Boundary of Graphs, Studia Math. Sci. Hungarica, (2001), 37,145-167, Math. Review number not available
  29. Varopoulos, R., Saloff-Coste, L., Coulhon, Th., (1993) Analysis and geometry on Groups, Cambridge University Press, 1993 Math. Review 95f:43008
  30. Varopoulos, R.Th., (1985) Hardy-Littlewood theory for semigroups, J. Functional Analysis 63, (1985) 215-239 Math. Review 87a:31011
  31. Woess, W., (1994) Random walks on infinite graphs and groups - a survey on selected topics, Bulletin of London Mathematical Society, 26, (1994),1-60 Math. Review 94i:60081
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