The Exact Hausdorff Dimension of a Branching Set
Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1993), article no. 7, 38 p. 
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     title = {The {Exact} {Hausdorff} {Dimension} of a {Branching} {Set}},
     journal = {Publications de l'Institut de recherche math\'ematiques de Rennes},
     eid = {7},
     pages = {1--38},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {2},
     year = {1993},
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     url = {http://archive.numdam.org/item/PSMIR_1993___2_A7_0/}
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Liu, Quansheng. The Exact Hausdorff Dimension of a Branching Set. Publications de l'Institut de recherche mathématiques de Rennes, Fascicule de probabilités, no. 2 (1993), article  no. 7, 38 p. http://archive.numdam.org/item/PSMIR_1993___2_A7_0/

[1] K.B. Athreya and P.E. Ney. Branching processes. Spring-Verlag, 1972. | MR | Zbl

[2] A.S. Besicovitch. On the fundamental geometrical properties of linearly measurable plan sets of points. Mathematische Annalen. 98 (1928) 422-64. | JFM | MR

[3] K.J. Falconer. The Geometry of Fractal Sets. Cambridge Univ. Press, 1985 | MR | Zbl

[4] K.J. Falconer. Random fractals, Math. Proc. Camb. Phil. Soc. 100 (1986) 559-582. | MR | Zbl

[5] K.J. Falconer. Cut set sums and tree processes. Proc. Amer. Math. Soc., (2) 101 (1987) 337-346. | MR | Zbl

[6] K.J. Falconer. Fractal Geometry. John Wiley & Sons Ltd, 1990. | MR | Zbl

[7] S. Graf, R.D. Maudin and S.C. Williams. The exact Hausdorff dimension in random recursive constructions. Mem. Amer. Math. Soc., 71 (1988), No. 381. | MR | Zbl

[8] J. Hawkes. Trees generated by a simple branching process. J. London Math. Soc. (2) 24 (1981) 373-384. | MR | Zbl

[9] J.P. Kahane, J. Peyrière, Sur certaines martingales de B. Mandelbrot, Adv. Math. 22 (1976) 131-145. | MR | Zbl

[10] Q. Liu. Sur quelques problèmes à propos des processus de branchement, des flots dans les réseaux et des mesures de Hausdorff associées. Thèse de doctorat de L'Université Paris 6, Laboratoire de Probabilités, Paris, 1993.

[11] R. Lyons. Random walks and percolation on trees. Ann. of Probab. 18 (1990) 931-952 | MR | Zbl

[12] R. Lyons and R. Pemantle. Random walk in a random environment and first passage percolation on trees. Ann. of probab. 20, (1992) 125-135. | MR | Zbl

[13] R. Lyons, R. Pemantle and Y. Peres. Ergodic theory on Galton-Watson trees, I: Speed of random walk and dimension of Harmonic measure. preprint, 1993. | MR | Zbl

[14] R.D. Maudin and S.C. Williams. Random constructions, Asympototic geometric and topological properties. Trans. Amer. Math. Soc. 295 (1986), 325-346. | MR | Zbl

[15] J. Neveu. Arbre et processus de Galton-Watson, Ann. Inst. Henri Poincaré, 22 (1986), 199-207. | Numdam | MR | Zbl

[16] C.A. Rogers. Hausdorff Measures, Cambridge Univ. Press, 1970. | MR | Zbl

[17] S.J. Taylor. The measure theory of random fractals, Math. Proc. Cambridge Philos. Soc. 100 (1986), 383-406. | MR | Zbl