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References

  1. S. Alexander and R. Orbach. Density of states on fractals: ``fractons''. J. Physique (Paris) Lett. 43 (1982), L625-L631.
  2. K. B. Athreya and P. E. Ney. Branching processes. Springer-Verlag, New York, 1972, Die Grundlehren der mathematischen Wissenschaften, Band 196. MR0373040
  3. M. T. Barlow and R. F. Bass. The construction of Brownian motion on the Sierpinski carpet. Ann. Inst. H. Poincare Probab. Statist. 25 (1989), no. 3, 225-257. MR1023950
  4. M. T. Barlow, A. A. Jarai, T. Kumagai, and G. Slade. Random walk on the incipient infinite cluster for oriented percolation in high dimensions. Comm. Math. Phys. 278 (2008), 385-31. MR2372764
  5. M. T. Barlow and T. Kumagai. Random walk on the incipient infinite cluster on trees. Illinois J. Math. 50 (2006), no. 1-4, 33-65 (electronic). MR2247823
  6. T. Duquesne. Continuum random trees and branching processes with immigration. Preprint available at arXiv:math/0509519.
  7. T. Duquesne and J.-F. Le Gall. The Hausdorff measure of stable trees. ALEA 1 (2006), 393--415. MR2291942
  8. W. Feller. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons Inc., New York, 1966. MR0270403
  9. K. Fleischmann, V. A. Vatutin, and V. Wachtel. Critical Galton-Watson processes: the maximum of total progenies within a large window. Preprint available at arXiv:math/0601333.
  10. I. Fujii and T. Kumagai. Heat kernel estimates on the incipient infinite cluster for critical branching processes. Proceedings of German-Japanese symposium in Kyoto 2006, RIMS Kokyuroku Bessatsu B6 (2008), 85-95.
  11. R. van der Hofstad, F. den Hollander, and G. Slade. Construction of the incipient infinite cluster for spread-out oriented percolation above 4+1 dimensions. Comm. Math. Phys. 231 (2002), no. 3, 435-461. MR1946445
  12. R. van der Hofstad and A. A. Jarai. The incipient infinite cluster for high-dimensional unoriented percolation. J. Statist. Phys. 114 (2004), no. 3-4, 625-663. MR2035627
  13. B. D. Hughes. Random Walks and Random Environments. Vol. 2: Random Environments. Oxford University Press, Oxford, 1996. MR1420619
  14. H. Kesten. Sub-diffusive behavior of random walk on a random cluster. Ann. Inst. H. Poincare Probab. Statist. 22 (1986), no. 4, 425--487. MR2372764
  15. H. Kesten. Sub-diffusive behavior of random walk on a random cluster. Unpublished proof.
  16. T. Kumagai and J. Misumi. Heat kernel estimates for strongly recurrent random walk on random media. To appear in J. Theoret. Probab. Preprint available at arXix:0806.4507.
  17. J.-F. Le Gall. Random real trees. Ann. Fac. Sci. Toulouse Math. (6) 15 (2006), no. 1, 35-62. MR2225746
  18. A. G. Pakes, Some new limit theorems for the critical branching process allowing immigration. Stochastic Processes Appl. 4 (1976), no. 2, 175-185. MR0397912
  19. E. Seneta. Regularly varying functions. Springer-Verlag, Berlin, 1976, Lecture Notes in Mathematics, Vol. 508. MR0453936
  20. R. S. Slack. A branching process with mean one and possibly infinite variance. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 (1968), 139-145. MR0228077
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