The diminishing segment process |
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| Authors: | Gergely Ambrus Viktor Vígh |
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| Institution: | a Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungaryb Centro de Investigación en Matemáticas, Jalisco S/N, Valenciana, Guanajuato, GTO 36240, Mexicoc Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW Calgary, AB, Canada T2N 1N4 |
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| 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. |
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| Keywords: | Arcsine law Continuous state space Markov chain Poisson-Dirichlet law Intersection of convex discs |
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