The Exact Hausdorff Dimension of a Branching Set

Quansheng Liu

Publications mathématiques et informatique de Rennes (1993)

  • Issue: 2, page 1-38

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Liu, Quansheng. "The Exact Hausdorff Dimension of a Branching Set." Publications mathématiques et informatique de Rennes (1993): 1-38. <http://eudml.org/doc/274010>.

@article{Liu1993,
author = {Liu, Quansheng},
journal = {Publications mathématiques et informatique de Rennes},
language = {eng},
number = {2},
pages = {1-38},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {The Exact Hausdorff Dimension of a Branching Set},
url = {http://eudml.org/doc/274010},
year = {1993},
}

TY - JOUR
AU - Liu, Quansheng
TI - The Exact Hausdorff Dimension of a Branching Set
JO - Publications mathématiques et informatique de Rennes
PY - 1993
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - 2
SP - 1
EP - 38
LA - eng
UR - http://eudml.org/doc/274010
ER -

References

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  1. [1] K.B. Athreya and P.E. Ney. Branching processes. Spring-Verlag, 1972. Zbl0259.60002MR373040
  2. [2] A.S. Besicovitch. On the fundamental geometrical properties of linearly measurable plan sets of points. Mathematische Annalen.98 (1928) 422-64. MR1512414JFM53.0175.04
  3. [3] K.J. Falconer. The Geometry of Fractal Sets. Cambridge Univ. Press, 1985 Zbl0587.28004MR867284
  4. [4] K.J. Falconer. Random fractals, Math. Proc. Camb. Phil. Soc.100 (1986) 559-582. Zbl0623.60020MR857731
  5. [5] K.J. Falconer. Cut set sums and tree processes. Proc. Amer. Math. Soc., (2) 101 (1987) 337-346. Zbl0636.90031MR902553
  6. [6] K.J. Falconer. Fractal Geometry. John Wiley & Sons Ltd, 1990. Zbl0689.28003MR3236784
  7. [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. Zbl0641.60003MR920961
  8. [8] J. Hawkes. Trees generated by a simple branching process. J. London Math. Soc. (2) 24 (1981) 373-384. Zbl0468.60081MR631950
  9. [9] J.P. Kahane, J. Peyrière, Sur certaines martingales de B. Mandelbrot, Adv. Math.22 (1976) 131-145. Zbl0349.60051MR431355
  10. [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. [11] R. Lyons. Random walks and percolation on trees. Ann. of Probab.18 (1990) 931-952 Zbl0714.60089MR1062053
  12. [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. Zbl0751.60066MR1143414
  13. [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. Zbl0819.60077MR1336708
  14. [14] R.D. Maudin and S.C. Williams. Random constructions, Asympototic geometric and topological properties. Trans. Amer. Math. Soc.295 (1986), 325-346. Zbl0625.54047MR831202
  15. [15] J. Neveu. Arbre et processus de Galton-Watson, Ann. Inst. Henri Poincaré, 22 (1986), 199-207. Zbl0601.60082MR850756
  16. [16] C.A. Rogers. Hausdorff Measures, Cambridge Univ. Press, 1970. Zbl0915.28002MR281862
  17. [17] S.J. Taylor. The measure theory of random fractals, Math. Proc. Cambridge Philos. Soc.100 (1986), 383-406. Zbl0622.60021MR857718

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