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References

  • E. Aïdékon: Speed of the biased random walk on a Galton–Watson tree. Probab. Theory Related Fields 159 (2014), no. 3-4, 597--617. MR3230003
  • K. B. Athreya, P. E. Ney: Branching processes. Die Grundlehren der mathematischen Wissenschaften, Band 196. Springer-Verlag, New York-Heidelberg, 1972. xi+287 pp. MR0373040
  • G. Ben Arous, A. Fribergh, and V. Sidoravicius: A proof of the Lyons-Pemantle-Peres monotonicity conjecture for high biases, to appear in Communications in Pure and Applied Mathematics. arXiv:1111.5865
  • N. H. Bingham, C. M. Goldie, and J. L. Teugels: Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871
  • N. Curien, J.-F. Le Gall: The harmonic measure of balls in random trees, preprint 2013, arxiv:1304.7190
  • T. Duquesne, J.-F. Le Gall: Random trees, Lévy processes and spatial branching processes. Astérisque No. 281 (2002), vi+147 pp. MR1954248
  • T. Duquesne, J.-F. Le Gall: The Hausdorff measure of stable trees, Alea Lat. Am. J. Probab. Math. Stat., 1 (2006), 393-415. MR2291942
  • W. Feller: An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403
  • K. Fleĭshmann, V. A. Vatutin, and V. Wachtel: Critical Galton-Watson branching processes: the maximum of the total number of particles within a large window. (Russian) Teor. Veroyatn. Primen. 52 (2007), no. 3, 419--445; translation in Theory Probab. Appl. 52 (2008), no. 3, 470--492 MR2743023
  • J.-F. Le Gall: Random trees and applications. Probab. Surv. 2 (2005), 245--311. MR2203728
  • S. Lin: Tree-indexed random walk and random walk on trees, PhD Thesis, Université Paris-Sud XI, 2014.
  • R. Lyons, R. Pemantle, and Y. Peres: Ergodic theory on Galton-Watson trees: speed of random walk and dimension of harmonic measure. Ergodic Theory Dynam. Systems 15 (1995), no. 3, 593--619. MR1336708
  • R. Lyons, R. Pemantle, and Y. Peres: Biased random walks on Galton-Watson trees, Probab. Theory Related Fields, 106 (1996), 249--264. MR1410689
  • R. Lyons and Y. Peres: Probability on Trees and Networks, Book in preparation, Current version available at http://mypage.iu.edu/~rdlyons/
  • B. Mehrdad, S. Sen, and L.-J. Zhu: The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias, to appear in Annales de l'Institut Henri Poincaré. arxiv:1212.3004
  • R. S. Slack: A branching process with mean one and possibly infinite variance. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 9 1968 139--145. MR0228077
  • V. A. Vatutin: Limit theorems for critical multitype Markov branching processes with infinite second moments. (Russian) Mat. Sb. (N.S.) 103(145) (1977), no. 2, 253--264, 319. MR0443115
  • A. L. Yakymiv: Reduced branching processes. (Russian) Teor. Veroyatnost. i Primenen. 25 (1980), no. 3, 593--596; translation in Theory Probab. Appl. 25 (1980), no. 3, 584–588.MR0582588


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