When Does the Union of Random Spherical Caps Become Connected?
نویسنده
چکیده
Drop N random caps all of the same angular radius θ = c √ 1 N logN on a unit sphere. Let U denote the part of the surface covered by these caps. We prove that if c > √ 2, then the probability that U is connected tends to 1 as N → ∞, while if c < 1, then the probability that U is connected tends to 0 as N → ∞.
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تاریخ انتشار 2004