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

Abstract

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 $\frac{Np}{\log N}\le 1/2$ a partition of the surface of sphere is remains uncovered by the $N$ caps almost surely.

Cited by in corpus (1)

• Number of Edges in Random Intersection Graph on Surface of a Sphere