Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T03:18:36.029Z Has data issue: false hasContentIssue false
  • English
  • Français

Random dissections and branching processes

Published online by Cambridge University Press:  24 October 2008

J. F. C. Kingman
J. F. C. Kingman
Affiliation:
University of Bristol
Get access Rights & Permissions [Opens in a new window]

Extract

For a time in the mid-1970s probabilists were tantalized by a seemingly simple problem posed by Araki and Kakutani[3]. An interval is repeatedly divided by points chosen successively at random, the nth point being uniformly distributed over the largest of the n intervals formed by the first n − 1 points. Is this sequence of points asymptotically uniformly distributed?

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 1 , July 1988 , pp. 147 - 151
Copyright
Copyright © Cambridge Philosophical Society 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Crump, K. S. and Mode, C. J.. A general age-dependent branching process. J. Math. Anal. Appl. 24 (1968), 494–508.CrossRefGoogle Scholar
Crump, K. S. and Mode, C. J.. A general age-dependent branching process. J. Math. Anal. Appl. 25 (1969), 8–17.CrossRefGoogle Scholar
[2]Ganuza, E. Z. and Durham, S. D.. Mean-square and almost-sure convergence of supercritical age-dependent branching processes. J. Appl. Prob. 11 (1974), 678–686.CrossRefGoogle Scholar
[3]Kakutani, S.. A problem in equidistribution. In Probabilistic Methods in Differential Equations, Lecture Notes in Math. vol. 451 (Springer-Verlag, 1975), pp. 369–376.Google Scholar
[4]Slud, E. V.. Entropy and maximal spacings for random partitions. Z. Wahrsch. Verw. Gebiete 41 (1977/1978), 341–352.CrossRefGoogle Scholar
[5]Van Zwet, W. R.. A proof of Kakutani's conjecture on random subdivision of longest intervals. Ann. Probab. 6 (1978), 133–137.Google Scholar