The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. D. Aldous. The continuum random tree. I. Ann. Probab., 19(1):1--28, 1991. Math. Review 91i:60024
  2. D. Aldous. The continuum random tree. III. Ann. Probab., 21(1):248--289, 1993. Math. Review 94c:60015
  3. D. Aldous. Probability distributions on cladograms. In Random discrete structures (Minneapolis, MN, 1993), volume 76 of IMA Vol. Math. Appl., pages 1--18. Springer, New York, 1996. Math. Review 98d:60018
  4. J. Bertoin. Homogeneous fragmentation processes. Probab. Theory Related Fields, 121(3):301--318, 2001. Math. Review 2002j:60127
  5. J. Bertoin. Self-similar fragmentations. Ann. Inst. H. Poincaré Probab. Statist., 38(3):319--340, 2002. Math. Review 2003h:60109
  6. J. Bertoin. Random fragmentation and coagulation processes, volume 102 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2006. Math. Review 2007k:60004
  7. T. Duquesne and J.-F. Le Gall. Random trees, Lévy processes and spatial branching processes. Astérisque, (281):vi+147, 2002. Math. Review 2003m:60239
  8. T. Duquesne and J.-F. Le Gall. Probabilistic and fractal aspects of Lévy trees. Probab. Theory Related Fields, 131(4):553--603, 2005. Math. Review 2006d:60123
  9. S. N. Evans, J. Pitman, and A. Winter. Rayleigh processes, real trees, and root growth with re-grafting. Probab. Theory Related Fields, 134(1):81--126, 2006. Math. Review 2007d:60003
  10. S. N. Evans and A. Winter. Subtree prune and regraft: a reversible real tree-valued Markov process. Ann. Probab., 34(3):918--961, 2006. Math. Review 2007k:60233
  11. W. Feller. An introduction to probability theory and its applications. Vol. I. Third edition. John Wiley & Sons Inc., New York, 1968. Math. Review 0228020
  12. D. J. Ford. Probabilities on cladograms: introduction to the alpha model. 2005. Preprint, arXiv:math.PR/0511246. Math. Review number not available.
  13. A. Greven, P. Pfaffelhuber, and A. Winter. Convergence in distribution of random metric measure spaces (Lambda-coalescent measure trees). Probability Theory and Related Fields -- Online First, DOI 10.1007/s00440-008-0169-3, 2008. Math. Review number not available.
  14. R. C. Griffiths. Allele frequencies with genic selection. J. Math. Biol., 17(1):1--10, 1983. Math. Review 84h:92019
  15. B. Haas and G. Miermont. The genealogy of self-similar fragmentations with negative index as a continuum random tree. Electron. J. Probab., 9:no. 4, 57--97 (electronic), 2004. Math. Review 2004m:60086
  16. B. Haas, G. Miermont, J. Pitman, and M. Winkel. Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models. Ann. Probab., 36(5):1790--1837, 2008. Math. Review 2440924
  17. B. Haas, J. Pitman, and M. Winkel. Spinal partitions and invariance under re-rooting of continuum random trees. Preprint, arXiv:0705.3602, 2007, to appear in Annals of Probability. Math. Review number not available.
  18. D. E. Knuth. The art of computer programming. Vol. 1: Fundamental algorithms. Second printing. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969. Math. Review 0286317
  19. P. Marchal. A note on the fragmentation of a stable tree. In Fifth Colloquium on Mathematics and Computer Science, volume AI, pages 489--500. Discrete Mathematics and Theoretical Computer Science, 2008. Math. Review number not available.
  20. P. McCullagh, J. Pitman, and M. Winkel. Gibbs fragmentation trees. Bernoulli, 14(4):988--1002, 2008. Math. Review number not available.
  21. G. Miermont. Self-similar fragmentations derived from the stable tree. I. Splitting at heights. Probab. Theory Related Fields, 127(3):423--454, 2003. Math. Review 2005m:60163
  22. G. Miermont. Self-similar fragmentations derived from the stable tree. II. Splitting at nodes. Probab. Theory Related Fields, 131(3):341--375, 2005. Math. Review 2006e:60107
  23. J. Pitman. Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2006. Lectures from the 32nd Summer School on Probability Theory held in Saint-Flour, July 7--24, 2002. Math. Review 2008c:60001
  24. J. Pitman and M. Winkel. Regenerative tree growth: binary self-similar continuum random trees and Poisson-Dirichlet compositions. Preprint, arXiv:0803.3098, 2008, to appear in Annals of Probability. Math. Review number not available.
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.