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Volumn 26, Issue 4, 1998, Pages 1703-1726

The standard additive coalescent

Author keywords

Brownian excursion; Continuum random tree; Random forest; Splitting; Stable subordinator; Stochastic coalescence; Stochastic fragmentation

Indexed keywords


EID: 0032237324     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1022855879     Document Type: Article
Times cited : (119)

References (35)
  • 1
    • 0001429918 scopus 로고
    • Stopping times and tightness II
    • ALDOUS, D. (1989). Stopping times and tightness II. Ann. Probab. 17 586-595.
    • (1989) Ann. Probab. , vol.17 , pp. 586-595
    • Aldous, D.1
  • 2
    • 0001981461 scopus 로고
    • The continuum random tree I
    • ALDOUS, D. (1991). The continuum random tree I. Ann. Probab. 19 1-28.
    • (1991) Ann. Probab. , vol.19 , pp. 1-28
    • Aldous, D.1
  • 3
    • 0001812090 scopus 로고
    • The continuum random tree II: An overview
    • (M. Barlow and N. Bingham, eds.) Cambridge Univ. Press
    • ALDOUS, D. (1991). The continuum random tree II: an overview. In Stochastic Analysis (M. Barlow and N. Bingham, eds.) 23-70. Cambridge Univ. Press.
    • (1991) Stochastic Analysis , pp. 23-70
    • Aldous, D.1
  • 4
    • 0003296611 scopus 로고
    • The continuum random tree III
    • ALDOUS, D. (1993). The continuum random tree III. Ann. Probab. 21 248-289.
    • (1993) Ann. Probab. , vol.21 , pp. 248-289
    • Aldous, D.1
  • 5
    • 0040847184 scopus 로고
    • Recursive self-similarity for random trees, random triangulations and Brownian excursion
    • ALDOUS, D. (1994). Recursive self-similarity for random trees, random triangulations and Brownian excursion. Ann. Probab. 22 527-545.
    • (1994) Ann. Probab. , vol.22 , pp. 527-545
    • Aldous, D.1
  • 6
    • 0031483018 scopus 로고    scopus 로고
    • Brownian excursions, critical random graphs and the multiplicative coalescent
    • ALDOUS, D. (1997). Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab. 25 812-854.
    • (1997) Ann. Probab. , vol.25 , pp. 812-854
    • Aldous, D.1
  • 7
    • 0003268734 scopus 로고    scopus 로고
    • Deterministic and stochastic models for coalescence: A review of the mean-field theory for probabilists
    • To appear
    • ALDOUS, D. (1997). Deterministic and stochastic models for coalescence: a review of the mean-field theory for probabilists. Bernoulli. To appear. Available via http://www. stat.berkeley.edu/users/aldous.
    • (1997) Bernoulli
    • Aldous, D.1
  • 8
    • 84990663423 scopus 로고
    • Brownian bridge asymptotics for random mappings
    • ALDOUS, D. and PITMAN, J. (1994). Brownian bridge asymptotics for random mappings. Random Structures Algorithms 5 487-512.
    • (1994) Random Structures Algorithms , vol.5 , pp. 487-512
    • Aldous, D.1    Pitman, J.2
  • 9
    • 0039660978 scopus 로고    scopus 로고
    • Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent
    • Dept. Statistics, Univ. California, Berkeley
    • ALDOUS, D. and PITMAN, J. (1998). Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent. Technical Report 525, Dept. Statistics, Univ. California, Berkeley. Available via http://www.stat.berkeley.edu/users/pitman.
    • (1998) Technical Report , vol.525
    • Aldous, D.1    Pitman, J.2
  • 10
    • 38249024666 scopus 로고
    • Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex
    • DONNELLY, P. and JOYCE, P. (1989). Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex. Stochastic Process. Appl. 31 89-103.
    • (1989) Stochastic Process. Appl. , vol.31 , pp. 89-103
    • Donnelly, P.1    Joyce, P.2
  • 11
    • 0039068872 scopus 로고
    • Conditioned limit theorems
    • DWASS, M. and KARLIN, S. (1963). Conditioned limit theorems. Ann. Math. Statist. 34 1147-1167.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 1147-1167
    • Dwass, M.1    Karlin, S.2
  • 13
    • 0039660979 scopus 로고    scopus 로고
    • Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent
    • To appear
    • EVANS, S. and PITMAN, J. (1997). Stationary Markov processes related to stable Ornstein-Uhlenbeck processes and the additive coalescent. Stoch. Process Appl. To appear. Available via http://www.stat.berkeley.edu/users/pitman.
    • (1997) Stoch. Process Appl.
    • Evans, S.1    Pitman, J.2
  • 14
    • 0032067120 scopus 로고    scopus 로고
    • Construction of Markovian coalescents
    • EVANS, S. and PITMAN, J. (1998). Construction of Markovian coalescents. Ann. Inst. H. Poincaré 34 339-383.
    • (1998) Ann. Inst. H. Poincaré , vol.34 , pp. 339-383
    • Evans, S.1    Pitman, J.2
  • 16
    • 21144463139 scopus 로고
    • The uniform random tree in a Brownian excursion
    • GALL, J.-F. L. (1993). The uniform random tree in a Brownian excursion. Probab. Theory Related Fields 96 369-384.
    • (1993) Probab. Theory Related Fields , vol.96 , pp. 369-384
    • Gall, J.-F.L.1
  • 18
    • 0000112160 scopus 로고
    • Brownian excursions, trees and measure-valued branching processes
    • GALL, J. L. (1991). Brownian excursions, trees and measure-valued branching processes. Ann. Probab. 19 1399-1439.
    • (1991) Ann. Probab. , vol.19 , pp. 1399-1439
    • Gall, J.L.1
  • 19
    • 0000658586 scopus 로고
    • The solution of the coagulating equation for cloud droplets in a rising air current
    • GOLOVIN, A. (1963). The solution of the coagulating equation for cloud droplets in a rising air current. Izv. Geophys. Ser. 5 482-487.
    • (1963) Izv. Geophys. Ser. , vol.5 , pp. 482-487
    • Golovin, A.1
  • 20
    • 0000647480 scopus 로고
    • Exact solutions for random coagulation processes
    • HENDRIKS, E., SPOUGE, J., EIBL, M. and SHRECKENBERG, M. (1985). Exact solutions for random coagulation processes. Z. Phys. B 58 219-227.
    • (1985) Z. Phys. B , vol.58 , pp. 219-227
    • Hendriks, E.1    Spouge, J.2    Eibl, M.3    Shreckenberg, M.4
  • 21
    • 0040847182 scopus 로고
    • A pair of conditional normal convergence theorems
    • KNIGHT, F. (1966). A pair of conditional normal convergence theorems. Theory Probab. Appl. 11 191-210.
    • (1966) Theory Probab. Appl. , vol.11 , pp. 191-210
    • Knight, F.1
  • 22
    • 0000991636 scopus 로고
    • Exponential families, extreme point models and minimal space-time invariant functions for stochastic processes with stationary and independent increments
    • KÜCHLER, U. and LAURITZEN, S. L. (1989). Exponential families, extreme point models and minimal space-time invariant functions for stochastic processes with stationary and independent increments. Scand. J. Statist. 16 237-261.
    • (1989) Scand. J. Statist. , vol.16 , pp. 237-261
    • Küchler, U.1    Lauritzen, S.L.2
  • 24
    • 0013484915 scopus 로고
    • A case of the limit distribution of the maximal volume on a tree in a random forest
    • PAVLOV, Y. (1979). A case of the limit distribution of the maximal volume on a tree in a random forest. Math. Notes of the Acad. Sci. USSR 25 387-392.
    • (1979) Math. Notes of the Acad. Sci. USSR , vol.25 , pp. 387-392
    • Pavlov, Y.1
  • 25
    • 38249001768 scopus 로고
    • Order statistics for jumps of normalized subordinators
    • PERMAN, M. (1993). Order statistics for jumps of normalized subordinators. Stochastic Process Appl. 46 267-281.
    • (1993) Stochastic Process Appl. , vol.46 , pp. 267-281
    • Perman, M.1
  • 26
    • 0001902647 scopus 로고
    • Size-biased sampling of Poisson point processes and excursions
    • PERMAN, M., PITMAN, J. and YOR, M. (1992). Size-biased sampling of Poisson point processes and excursions. Probab. Theory Related Fields 92 21-39.
    • (1992) Probab. Theory Related Fields , vol.92 , pp. 21-39
    • Perman, M.1    Pitman, J.2    Yor, M.3
  • 27
    • 0003848078 scopus 로고    scopus 로고
    • Coalescent random forests
    • To appear
    • PITMAN, J. (1996). Coalescent random forests. J. Combin. Theory Ser. A. To appear. Available via http://www.stat.berkeley.edu/users/pitman.
    • (1996) J. Combin. Theory Ser. A
    • Pitman, J.1
  • 28
    • 0001191605 scopus 로고    scopus 로고
    • Random discrete distributions invariant under size-biased permutation
    • PITMAN, J. (1996). Random discrete distributions invariant under size-biased permutation. Adv. in Appl. Probab. 28 525-539.
    • (1996) Adv. in Appl. Probab. , vol.28 , pp. 525-539
    • Pitman, J.1
  • 29
    • 85132282134 scopus 로고    scopus 로고
    • Partition structures derived from Brownian motion and stable subordinators
    • PITMAN, J. (1997). Partition structures derived from Brownian motion and stable subordinators. Bernoulli 3 79-96.
    • (1997) Bernoulli , vol.3 , pp. 79-96
    • Pitman, J.1
  • 30
    • 84962993911 scopus 로고
    • Arcsine laws and interval partitions derived from a stable subordinator
    • PITMAN, J. and YOR, M. (1992). Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc. 65 326-356.
    • (1992) Proc. London Math. Soc. , vol.65 , pp. 326-356
    • Pitman, J.1    Yor, M.2
  • 31
    • 0031534984 scopus 로고    scopus 로고
    • The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
    • PITMAN, J. and YOR, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 855-900.
    • (1997) Ann. Probab. , vol.25 , pp. 855-900
    • Pitman, J.1    Yor, M.2
  • 32
    • 0001939173 scopus 로고    scopus 로고
    • Coagulation and branching process models of gravitational clustering
    • SHETH, R. and PITMAN, J. (1997). Coagulation and branching process models of gravitational clustering. Mon. Not. Roy. Astron. Soc. 289 66-80.
    • (1997) Mon. Not. Roy. Astron. Soc. , vol.289 , pp. 66-80
    • Sheth, R.1    Pitman, J.2
  • 33
    • 0039738355 scopus 로고
    • Validity of the stochastic coagulation equation and runaway growth of protoplanets
    • TANAKA, H. and NAKAZAWA, K. (1994). Validity of the stochastic coagulation equation and runaway growth of protoplanets. Icarus 107 404-412.
    • (1994) Icarus , vol.107 , pp. 404-412
    • Tanaka, H.1    Nakazawa, K.2
  • 34
    • 0010067623 scopus 로고
    • Fluctuations in coagulating systems II
    • VAN DONGEN, P. (1987). Fluctuations in coagulating systems II. J. Statist. Phys. 49 927-975.
    • (1987) J. Statist. Phys. , vol.49 , pp. 927-975
    • Van Dongen, P.1


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