Discrete One-Dimensional Coverage Process on a Renewal Process
Consider the following coverage model on ℕ, for each site i∈ℕ associate a pair (ξ{sub i},R{sub i}) where (ξ{sub i}){sub i≥0} is a 1-dimensional undelayed discrete renewal point process and (R{sub i}){sub i≥0} is an i.i.d. sequence of ℕ-valued random variables. At each site where ξ{sub i}=1 start an interval of length R{sub i}. Coverage occurs if every site of ℕ is covered by some interval. We obtain sharp conditions for both, positive and null probability of coverage. As corollaries, we extend results of the literature of rumor processes and discrete one-dimensional Boolean percolation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗