A Strong threshold for the size of random caps to cover a sphere

Details A Strong threshold for the size of random caps to cover a sphere A Strong threshold for the size of random caps to cover a sphere

2008-09-06

arxiv.org/abs/0809.1142v1

Mathematics

Probability

Scientific paper

In this article, we consider `$N$'spherical caps of area $4\pi p$ 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 $\frac{Np}{\log\:N} > 1/2$ the surface of sphere is completely covered by the $N$ caps almost surely, and if $\frac{Np}{\log\:N} \leq 1/2$ a partition of the surface of sphere is remains uncovered by the $N$ caps almost surely.

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