Abstract
Arcs of lengthsl n, 0<l n+1<=l n<1,n=1,2,…, are thrown independently and uniformly on a circumferenceC of unit length. The union of the arcs coversC with probability one if and only if\(\sum\limits_{n = 1}^\infty {n^{ - 2} \exp \left( {l_1 + ... + 1l_n } \right) = \infty } \).
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Shepp, L.A. Covering the circle with random ARCS. Israel J. Math. 11, 328–345 (1972). https://doi.org/10.1007/BF02789327
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DOI: https://doi.org/10.1007/BF02789327