Strong threshold for the size of random caps to cover a sphere
نویسنده
چکیده
In this article, we consider ‘N ’spherical caps of area 4πp were uniformly distributed over the surface of a unit sphere. We are giving the strong threshold function for the size of random caps to cover the surface of a unit sphere. We have shown that for large N, if Np log N > 1/2 the surface of sphere is completely covered by the N caps almost surely , and if Np log N ≤ 1/2 a partition of the surface of sphere is remains uncovered by the N caps almost surely. AMS 2000 subject classifications: 05C80, 91D30.
منابع مشابه
A Threshold for the Size of Random Cover a Sphere
Consider a unit sphere on which are placed N random spherical caps of area 4rip(N). We prove that if lim (p(N).N/log N) < 1, then the probabil i ty that the sphere is completely covered by N caps tends to 0 as N--" 0% and if lim (p(N).N/ log N) > 1, then for any integer n > 0 the probabili ty that each point of the sphere is covered more than n times tends to 1 as N--* oo.
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