A THRESHOLD FOR THE SIZE OF RANDOM COVER A SPHERE
Hiroshi Maehara · 1988
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 for any integer n > 0 the probability that each point of the sphere is covered more than n times tends to 1 as N--* oo.