On point processes on the circle
Keyword(s):
Point processes on the circle with circumference 1 are considered, which are related to the coverage problem of the circle by n randomly placed arcs of a fixed length. The anticlockwise endpoint of each arc is assumed to be uniformly distributed on the circle. We deal with a general limit result on the convergence of these point processes to a Poisson process on the circle. This result is then applied to several cases of the coverage problem, giving improved limit results in these cases. The proof uses a new convergence result of general point processes.
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1975 ◽
Vol 7
(01)
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pp. 83-122
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Keyword(s):
1984 ◽
Vol 16
(02)
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pp. 324-346
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Keyword(s):
1986 ◽
Vol 18
(03)
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pp. 646-659
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