Let Xi(0) = vertical bar-1, 1 vertical bar, and define the segments Xi(n) recursively
in the following manner: for every n = 0,1.... let Xi(n+1) = Xi(n) boolean AND Xi(n)
boolean AND vertical bar a(n+1) - 1, a(n+1) + 1 vertical bar where the point a(n+1)
is chosen randomly on the segment Xi(n) with uniform distribution. For the radius
rho(n) of Xi(n) we prove that n(rho(n) - 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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