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Volumn 25, Issue 3, 2004, Pages 311-335

The shape of large Galton-Watson trees with possibly infinite variance

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EID: 11144340434     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/rsa.20021     Document Type: Article
Times cited : (13)

References (31)
  • 1
    • 0001324627 scopus 로고
    • Asymptotic fringe distributions for general families of random trees
    • D. Aldous, Asymptotic fringe distributions for general families of random trees, Ann Appl Probab 1 (1991), 228-266.
    • (1991) Ann Appl Probab , vol.1 , pp. 228-266
    • Aldous, D.1
  • 2
    • 0001812090 scopus 로고
    • The continuum random tree. II: An overview
    • Stochastic analysis (Durham, 1990), Cambridge University Press, Cambridge
    • D. Aldous, "The continuum random tree. II: An overview," Stochastic analysis (Durham, 1990), London Math Soc Lecture Note Ser 167, Cambridge University Press, Cambridge, 1991, pp. 23-70.
    • (1991) London Math Soc Lecture Note Ser , vol.167 , pp. 23-70
    • Aldous, D.1
  • 3
    • 0003296611 scopus 로고
    • The continuum random tree III
    • D. Aldous, The continuum random tree III, Ann Probab 21 (1993), 248-289.
    • (1993) Ann Probab , vol.21 , pp. 248-289
    • Aldous, D.1
  • 4
    • 0032165931 scopus 로고    scopus 로고
    • Tree-valued Markov chains derived from Gallon-Watson processes
    • D. Aldous and J. Pitman, Tree-valued Markov chains derived from Gallon-Watson processes, Ann Inst H Poincaré 34 (1998), 637-686.
    • (1998) Ann Inst H Poincaré , vol.34 , pp. 637-686
    • Aldous, D.1    Pitman, J.2
  • 6
    • 0034560041 scopus 로고    scopus 로고
    • A random walk approach to Gallon-Watson trees
    • J. Bennies and G. Kersting, A random walk approach to Gallon-Watson trees, J Theoret Probab 13 (2000), 777-803.
    • (2000) J Theoret Probab , vol.13 , pp. 777-803
    • Bennies, J.1    Kersting, G.2
  • 7
    • 0011634315 scopus 로고
    • On conditioning a random walk to stay positive
    • J. Bertoin and R. A. Doney, On conditioning a random walk to stay positive, Ann Probab 22 (1994), 2152-2167.
    • (1994) Ann Probab , vol.22 , pp. 2152-2167
    • Bertoin, J.1    Doney, R.A.2
  • 10
    • 0037758115 scopus 로고    scopus 로고
    • Large deviations
    • American Mathematical Society, Providence, RI
    • F. den Hollander, Large deviations, Fields Institute Monographs 14, American Mathematical Society, Providence, RI, 2000.
    • (2000) Fields Institute Monographs , vol.14
    • Den Hollander, F.1
  • 11
    • 0242337623 scopus 로고    scopus 로고
    • Branching processes and their applications in the analysis of tree structures and tree algorithms
    • Probabilistic methods for algorithmic discrete mathematics, Springer-Verlag, Berlin
    • L. Devroye, "Branching processes and their applications in the analysis of tree structures and tree algorithms," Probabilistic methods for algorithmic discrete mathematics, Algorithms Combin 16, Springer-Verlag, Berlin, 1998, pp. 249-314.
    • (1998) Algorithms Combin , vol.16 , pp. 249-314
    • Devroye, L.1
  • 12
    • 33947725198 scopus 로고    scopus 로고
    • Random trees, Levy processes and spatial branching processes
    • T. Duquesne and J.-F. Le Gall, Random trees, Levy processes and spatial branching processes, Astérisque 281 (2002).
    • (2002) Astérisque , vol.281
    • Duquesne, T.1    Le Gall, J.-F.2
  • 13
    • 0038336097 scopus 로고    scopus 로고
    • A limit theorem for the contour process of conditioned Galton-Watson trees
    • T. Duquesne, A limit theorem for the contour process of conditioned Galton-Watson trees, Ann Probab 31 (2003), 996-1027.
    • (2003) Ann Probab , vol.31 , pp. 996-1027
    • Duquesne, T.1
  • 14
    • 0009911678 scopus 로고
    • Some general results concerning the critical exponents of percolation processes
    • R. Durrett, Some general results concerning the critical exponents of percolation processes, Z Wahrscheinlichkeitstheor Verw Geb 69 (1985), 421-437.
    • (1985) Z Wahrscheinlichkeitstheor Verw Geb , vol.69 , pp. 421-437
    • Durrett, R.1
  • 15
    • 0001477232 scopus 로고
    • The total progeny in a branching process and a related random walk
    • M. Dwass, The total progeny in a branching process and a related random walk, J Appl Probab 6 (1969), 682-686.
    • (1969) J Appl Probab , vol.6 , pp. 682-686
    • Dwass, M.1
  • 16
    • 0141888171 scopus 로고    scopus 로고
    • A decomposition of the (1 + β)-superprocess conditioned on survival
    • A. M. Etheridge and D. R. E. Williams, A decomposition of the (1 + β)-superprocess conditioned on survival, Proc Roy Soc Edinburgh 133 (2003), 829-848.
    • (2003) Proc Roy Soc Edinburgh , vol.133 , pp. 829-848
    • Etheridge, A.M.1    Williams, D.R.E.2
  • 18
    • 0030604322 scopus 로고    scopus 로고
    • Size-biased and conditioned random splitting trees
    • J. Geiger, Size-biased and conditioned random splitting trees, Stochastic Process Appl 65 (1996), 187-207.
    • (1996) Stochastic Process Appl , vol.65 , pp. 187-207
    • Geiger, J.1
  • 19
    • 0033235812 scopus 로고    scopus 로고
    • Elementary new proofs of classical limit theorems for Galton-Watson processes
    • J. Geiger, Elementary new proofs of classical limit theorems for Galton-Watson processes, J Appl Probab 36 (1999), 301-309.
    • (1999) J Appl Probab , vol.36 , pp. 301-309
    • Geiger, J.1
  • 20
    • 11144328306 scopus 로고    scopus 로고
    • The Galton-Watson tree conditioned on its height
    • VSP, Utrecht
    • J. Geiger and G. Kersting, The Galton-Watson tree conditioned on its height, Proc 7th Vilnius Conf 1998, VSP, Utrecht, 1999, pp. 277-286.
    • (1999) Proc 7th Vilnius Conf 1998 , pp. 277-286
    • Geiger, J.1    Kersting, G.2
  • 23
    • 0042606570 scopus 로고
    • Exact distributions of kin numbers in Galton-Watson processes
    • A. Joffe and W. A. O'N. Waugh, Exact distributions of kin numbers in Galton-Watson processes, J Appl Probab 19 (1982), 767-775.
    • (1982) J Appl Probab , vol.19 , pp. 767-775
    • Joffe, A.1    Waugh, W.A.O'N.2
  • 24
    • 84985304761 scopus 로고
    • Stability of critical cluster fields
    • O. Kallenberg, Stability of critical cluster fields. Math Nachr 77 (1977), 7-43.
    • (1977) Math Nachr , vol.77 , pp. 7-43
    • Kallenberg, O.1
  • 25
    • 0001275106 scopus 로고
    • The Galton-Watson process conditioned on the total progeny
    • D. J. Kennedy, The Galton-Watson process conditioned on the total progeny, J Appl Probab 12 (1975), 800-806.
    • (1975) J Appl Probab , vol.12 , pp. 800-806
    • Kennedy, D.J.1
  • 27
    • 0000028988 scopus 로고
    • Conceptual proofs of L log L criteria for mean behavior of branching processes
    • R. Lyons, R. Pemantle, and Y. Peres, Conceptual proofs of L log L criteria for mean behavior of branching processes, Ann Probab 23 (1995), 1125-1138.
    • (1995) Ann Probab , vol.23 , pp. 1125-1138
    • Lyons, R.1    Pemantle, R.2    Peres, Y.3
  • 28
    • 0001270611 scopus 로고
    • On the altitude of nodes in random trees
    • A. Meir and J. W. Moon, On the altitude of nodes in random trees, Canad J Math 30 (1978), 997-1015.
    • (1978) Canad J Math , vol.30 , pp. 997-1015
    • Meir, A.1    Moon, J.W.2
  • 29
    • 0000458044 scopus 로고
    • Abres et processus de Galton-Watson
    • J. Neveu, Abres et processus de Galton-Watson, Ann Inst H Poincaré 22 (1986), 199-207.
    • (1986) Ann Inst H Poincaré , vol.22 , pp. 199-207
    • Neveu, J.1
  • 30
    • 0000898137 scopus 로고    scopus 로고
    • Enumerations of trees and forests related to branching processes and random walks
    • J. Pitman, Enumerations of trees and forests related to branching processes and random walks, DIMACS Ser Discrete Math Theoret Comput Sci 41 (1998), 163-180.
    • (1998) DIMACS Ser Discrete Math Theoret Comput Sci , vol.41 , pp. 163-180
    • Pitman, J.1
  • 31
    • 0242337620 scopus 로고
    • The asymptotic distribution of the total heights of random rooted trees
    • L. Takács, The asymptotic distribution of the total heights of random rooted trees, Acta Sci Math 57 (1993), 613-625.
    • (1993) Acta Sci Math , vol.57 , pp. 613-625
    • Takács, L.1


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