no. 2
Local dimensions of the branching measure on a Galton-Watson tree
Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 195-222. 
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     author = {Liu, Quansheng},
     title = {Local dimensions of the branching measure on a {Galton-Watson} tree},
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     pages = {195--222},
     publisher = {Elsevier},
     volume = {37},
     number = {2},
     year = {2001},
     zbl = {0986.60080},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2001__37_2_195_0/}
}
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Liu, Quansheng. Local dimensions of the branching measure on a Galton-Watson tree. Annales de l'I.H.P. Probabilités et statistiques, Tome 37 (2001) no. 2, pp. 195-222. http://www.numdam.org/item/AIHPB_2001__37_2_195_0/

[1] N.H Bingham, On the limit of a supercritical branching process, J. Appl. Prob. 25A (1988) 215-228. | MR | Zbl

[2] N.H Bingham, R.A Doney, Asymptotic properties of supercritical branching processes I: The Galton-Watson process, Adv. Appl. Prob. 6 (1974) 711-731. | MR | Zbl

[3] Y.S Chow, H Teicher, Probability: Independence, Interchageability and Martingales, Springer-Verlag, New York, 1978. | MR | Zbl

[4] C.S Dai, S.J Taylor, Defining fractals in a probability space, Ill. J. Math. 38 (1994) 480-500. | MR | Zbl

[5] A De Meyer, On a theorem of Bingham and Doney, J. Appl. Prob. 19 (1982) 217-220. | MR | Zbl

[6] J.C D'Souza, The extinction time of the inhomogeneous branching Process, in: Heyde C.C (Ed.), Branching Processes: Proc. First World Congress, Lecture Notes in Statistics, 99, Springer, Berlin, 1995, pp. 106-117. | MR | Zbl

[7] T.E Harris, Branching Processes, Springer-Verlag, 1963. | MR | Zbl

[8] J Hawkes, A lower Lipschitz condition for the stable subordinator, Z. Wahr. verw. Geb. 17 (1971) 23-32. | MR | Zbl

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

[10] X Hu, S.J Taylor, The multifractal structure of stable occupation measure, Stoch. Proc. Appl. 66 (1997) 283-299. | MR | Zbl

[11] A Joffe, Remarks on the structure of trees with applications to supercritical Galton-Watson processes, in: Joffe A, Ney P (Eds.), Advances in Prob., 5, Dekker, New-York, 1978, pp. 263-268. | MR | Zbl

[12] P Lévy, Théorie de l'Addition des Variables Aléatoires, Gautier-Villars, Paris, 1954. | JFM

[13] Q.S Liu, The exact Hausdorff dimension of a branching set, Prob. Theory Related Fieds 104 (1996) 515-538. | MR | Zbl

[14] Q.S Liu, The growth of an entire characteristic function and the tail probabilities of the limit of a tree martingale, Trees, in: Chauvin B, Cohen S, Rouault A (Eds.), Trees, Progress in Probability, 40, Birkhäuser, Basel, 1996, pp. 51-80. | MR | Zbl

[15] Q.S Liu, Exact packing measure of the boundary of a Galton-Watson tree, Stoch. Proc. Appl. 85 (2000) 19-28. | MR | Zbl

[16] Q.S Liu, A Rouault, On two measures defined on the boundary of a branching tree, in: Athreya K.B, Jagers P (Eds.), Classical and Modern Branching Processes, IMA Volumes in Mathematics and its Applications, 84, Springer-Verlag, 1996, pp. 187-202. | MR | Zbl

[17] Q.S Liu, N.R Shieh, A uniform limit law for the branching measure on a Galton-Watson tree, Asian J. Math. 3 (1999) 381-386. | MR | Zbl

[18] R Lyons, R Pemantle, Y Peres, Ergodic theory on Galton-Watson trees, Speed of random walk and dimension of harmonic measure, Ergodic Theory Dynamical Systems 15 (1995) 593-619. | MR | Zbl

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

[20] G.L O'Brien, A limit theorem for sample maxima and heavy branches in Galton-Watson trees, J. Appl. Prob. 17 (1980) 539-545. | MR | Zbl

[21] B Ramachandran, On the order and the type of entire characteristic functions, Ann. Stat. 33 (1962) 1238-1255. | MR | Zbl

[22] N.R Shieh, S.J Taylor, Logarithmic multifractal spectrum of stable occupation measure, Stoch. Proc. Appl. 75 (1998) 249-261. | MR | Zbl

[23] N.R Shieh, S.J Taylor, Multifractal spectra of branching measure on a Galton-Watson tree, Preprint, 1999. | MR