A family of random trees with random edge lengths

Random Structures and Algorithms

Volumn 15, Issue 2, 1999, Pages 176-195

  Aldous, David ^a   Pitman, Jim ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Cayley's multinomial expansion; Continuum tree; Enumeration; Random tree; Spanning tree; Weighted tree

Indexed keywords

EID: 0033434863     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199909)15:2<176::AID-RSA4>3.0.CO;2-4     Document Type: Article

References (24)

1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
2. D.J. Aldous, The continuum random tree III, Ann Probab 21 (1993) 248-289.
3. D.J. Aldous and J. Pitman, Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent, Technical Report 525, Dept. Statistics, U.C. Berkeley, 1998. To appear in PTRF. Available via homepage http://www.stat.berkeley.edu/ users/aldous.
4. D.J. Aldous and J. Pitman, The standard additive coalescent, Ann Probab 26 (1998), 1703-1726.
5. L. Alonso and R. Schott, Random Generation of Trees, Kluwer, Dordrecht, 1995.
6. M. Camarri and J. Pitman, Limit distributions and random trees derived from the birthday problem with unequal probabilities. Technical Report 523, Dept. Statistics, U.C. Berkeley, 1998. To appear in Electronic J Probab. Available via http://www.stat.berkeley. edu/users/pitman.
7. A. Cayley, A theorem on trees, Quarterly J Pure Appl Math 23 (1889), 376-378 (Also in The Collected Mathematical Papers of Arthur Cayley, Cambridge University Press, Cambridge, 1897), Vol XIII, pp. 26-28.
8. A. Cayley, A theorem on trees, Quarterly J Pure Appl Math 23 (1889), 376-378 (Also in The Collected Mathematical Papers of Arthur Cayley, Cambridge University Press, Cambridge, 1897), Vol XIII, pp. 26-28.
9. R. Durrett, H. Kesten, and E. Waymire, On weighted heights of random trees, J Theoret Probab 4 (1991), 223-237.
10. E.N. Gilbert and H.O. Pollak, Steiner minimal trees, SIAM J Appl Math. 16 (1968), 1-29.
11. F.K. Hwang, D.S. Richards, and P. Winter, The Steiner Tree Problem, Vol. 53 of Annals of Discrete Mathematics, North Holland, Amsterdam, 1992.
12. D.E. Knuth, The Art of Computer Programming, Addison-Wesley, Reading, MA, 1968, Vol. 1.
13. W.P. Maddison and M. Slatkin, Null models for the number of evolutionary steps in a character on a phylogenic tree, Evolution 45 (1991), 1184-1197.
14. H.M. Mahmoud, Evolution of Random Search Trees, Wiley, New York, 1992.
15. J.W. Moon, Counting Labelled Trees, Canadian Mathematical Congress, 1970, Canadian Mathematical Monographs No. 1.
16. J. Pitman, Exchangeable and partially exchangeable random partitions, Probab Theory Relat Fields 102 (1995), 145-158.
17. J. Pitman Abel-Cayley-Hurwitz multinomial expansions associated with random mappings, forests and subsets, Technical Report 498, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley.edu/users/pitman.
18. J. Pitman, Partition structures derived from Brownian motion and stable subordinators, Bernoulli 3 (1997) 79-96.
19. J. Pitman, The asymptotic behavior of the Hurwitz binomial distribution, Technical Report 500, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley. edu/users/pitman. To appear in Combinatorics, Probab, Computing.
20. J. Pitman, The multinomial distribution on rooted labeled forests, Technical Report 499, Dept. Statistics, U.C. Berkeley, 1997. Available via http://www.stat.berkeley. edu/users/pitman.
21. J. Pitman, Coalescent random forests, J Comb Theory A 85 (1999) 165-193.
22. A Rényi, "On the enumeration of trees," in R. Guy, H. Hanani, N. Sauer, and J. Schonheim (Editors), Combinatorial Structures and their Applications. Gordon and Breach, New York, 1970, pp. 355-360.
23. J.M. Steele, Probability Theory and Combinatorial Optimization, Number 69 in CBMS-NSF Regional Conference Series in Applied Math SIAM, 1997.
24. S. Tavaré, Line-of-descent and genealogical processes and their applications in population genetics, Theoret Population Biol 26 (1984), 119-164.