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Volumn 17, Issue 2, 2000, Pages 79-102

On a random graph with immigrating vertices: Emergence of the giant component

Author keywords

Branching markov chain; Giant component; Martingale; Multiplicative coalescent; Random graph; Weak convergence correspondence to

Indexed keywords


EID: 0034401314     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/1098-2418(200009)17:2<79::AID-RSA1>3.0.CO;2-W     Document Type: Article
Times cited : (27)

References (19)
  • 1
    • 0031483018 scopus 로고    scopus 로고
    • Brownian excursions, critical random graphs and the multiplicative coalescent
    • D.J. Aldous, Brownian excursions, critical random graphs and the multiplicative coalescent, Ann Probab 25 (1997), 812-854.
    • (1997) Ann Probab , vol.25 , pp. 812-854
    • Aldous, D.J.1
  • 2
    • 0032342037 scopus 로고    scopus 로고
    • Emergence of the giant component in special Marcus-Lushnikov processes
    • D.J. Aldous, Emergence of the giant component in special Marcus-Lushnikov processes, Random Struct Algorithms 12 (1998), 179-196.
    • (1998) Random Struct Algorithms , vol.12 , pp. 179-196
    • Aldous, D.J.1
  • 3
    • 0003300947 scopus 로고    scopus 로고
    • The entrance boundary of the multiplicative coalescent
    • D.J. Aldous and V. Limic, The entrance boundary of the multiplicative coalescent, Electron J Probab 3 (1998), 1-59.
    • (1998) Electron J Probab , vol.3 , pp. 1-59
    • Aldous, D.J.1    Limic, V.2
  • 5
    • 0040982783 scopus 로고
    • Graph evolution by stochastic additions of points and lines
    • M. Capobianco and O. Frank, Graph evolution by stochastic additions of points and lines, Discrete Math 46 (1983), 133-143.
    • (1983) Discrete Math , vol.46 , pp. 133-143
    • Capobianco, M.1    Frank, O.2
  • 11
    • 0000976358 scopus 로고
    • On the behavior of a random graph near a critical point
    • V.F. Kolchin, On the behavior of a random graph near a critical point, Theory Probab Appl 31 (1986), 439-451.
    • (1986) Theory Probab Appl , vol.31 , pp. 439-451
    • Kolchin, V.F.1
  • 12
    • 0039203960 scopus 로고
    • Phase transition phenomena in random discrete structures
    • T. Łuczak, Phase transition phenomena in random discrete structures, Discrete Math 136 (1994), 225-242.
    • (1994) Discrete Math , vol.136 , pp. 225-242
    • ŁUczak, T.1
  • 13
    • 0001404742 scopus 로고
    • The structure of a random graph at the point of the phase transition
    • T. Łuczak, B. Pittel, and J.C. Wierman, The structure of a random graph at the point of the phase transition, Trans Am Math Soc 341 (1994), 721-748.
    • (1994) Trans Am Math Soc , vol.341 , pp. 721-748
    • ŁUczak, T.1    Pittel, B.2    Wierman, J.C.3
  • 14
    • 0033440601 scopus 로고    scopus 로고
    • Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent
    • J.R. Norris, Smoluchowski's coagulation equation: Uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent, Ann Appl Probab 9 (1999), 78-109.
    • (1999) Ann Appl Probab , vol.9 , pp. 78-109
    • Norris, J.R.1
  • 15
    • 0039203961 scopus 로고
    • A random graph with a subcritical number of edges
    • B. Pittel, A random graph with a subcritical number of edges, Trans Am Math Soc 309 (1988), 51-75.
    • (1988) Trans Am Math Soc , vol.309 , pp. 51-75
    • Pittel, B.1
  • 16
    • 84990635693 scopus 로고
    • On tree census and the giant component in sparse random graphs
    • B. Pittel, On tree census and the giant component in sparse random graphs, Random Struct Algorithms 1 (1990), 311-342.
    • (1990) Random Struct Algorithms , vol.1 , pp. 311-342
    • Pittel, B.1
  • 17
    • 0010687749 scopus 로고
    • Solutions and critical times for the monodisperse coagulation equation when a(i, j) = A + B(i + j) + Cij
    • J.L. Spouge, Solutions and critical times for the monodisperse coagulation equation when a(i, j) = A + B(i + j) + Cij, J Phys A Math Gen 16 (1983), 767-773.
    • (1983) J Phys A Math Gen , vol.16 , pp. 767-773
    • Spouge, J.L.1
  • 18
    • 0039080448 scopus 로고
    • Combinatorial algebra and random graphs
    • V.E. Stepanov, Combinatorial algebra and random graphs, Theory Probab Appl 14 (1969), 373-399.
    • (1969) Theory Probab Appl , vol.14 , pp. 373-399
    • Stepanov, V.E.1
  • 19
    • 0000198198 scopus 로고
    • On some features of the structure of a random graph near a critical point
    • V.E. Stepanov, On some features of the structure of a random graph near a critical point, Theory Probab Appl 32 (1988), 573-594.
    • (1988) Theory Probab Appl , vol.32 , pp. 573-594
    • Stepanov, V.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.