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Points P 1 ,. .. , P n in the unit square define a convex n-chain if they are below y = x and, together with P 0 = (0, 0) and P n+1 = (1, 1), they are in convex position. Under uniform probability, we prove an almost sure limit theorem for these chains that uses only probabilistic arguments, and which strengthens similar limit shape statements established… (More)

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