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The diminishing segment process

Author

Listed:
  • Ambrus, Gergely
  • Kevei, Péter
  • Vígh, Viktor

Abstract

Let Ξ0=[−1,1], and define the segments Ξn recursively in the following manner: for every n=0,1,…, let Ξn+1=Ξn∩[an+1−1,an+1+1], where the point an+1 is chosen randomly on the segment Ξn with uniform distribution. For the radius ρn of Ξn, we prove that n(ρn−1/2) converges in distribution to an exponential law, and we show that the centre of the limiting unit interval has arcsine distribution.

Suggested Citation

  • Ambrus, Gergely & Kevei, Péter & Vígh, Viktor, 2012. "The diminishing segment process," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 191-195.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:191-195
    DOI: 10.1016/j.spl.2011.09.016
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