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Fragment size distributions in random fragmentations with cutoff

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  • Ghorbel, M.
  • Huillet, T.

Abstract

We consider the following fragmentation model with cutoff: a fragment with initial size x0>1 splits into b>1 daughter fragments with random sizes, the partition law of which has exchangeable distribution. In subsequent steps, fragmentation proceeds independently for each sub-fragments whose sizes are bigger than some cutoff value xc=1 only. This process naturally terminates with probability 1. The size of a fragment is the random mass attached to a leaf of a "typical" path of the full (finite) fragmentation tree. The height's law of typical paths is first analyzed, using analytic and renewal processes techniques. We then compute fragments' size limiting distribution (x0[short up arrow][infinity]), for various senses of a typical path. Next, we exhibit some of its statistical features, essentially in the case of the exchangeable Dirichlet partition model.

Suggested Citation

  • Ghorbel, M. & Huillet, T., 2005. "Fragment size distributions in random fragmentations with cutoff," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 47-60, January.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:47-60
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    References listed on IDEAS

    as
    1. Hosam Mahmoud, 2003. "One-sided variations on binary search trees," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 885-900, December.
    2. Thierry Huillet & Servet Martinez, 2003. "Sampling from Finite Random Partitions," Methodology and Computing in Applied Probability, Springer, vol. 5(4), pages 467-492, December.
    3. Bertoin, J. & van Harn, K. & Steutel, F. W., 1999. "Renewal theory and level passage by subordinators," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 65-69, October.
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