Discrete One-Dimensional Coverage Process on a Renewal Process

Sandro Gallo and Nancy L. Garcia

Consider the following coverage model on N, for each site i ∈ N associate a pair (ξi, Ri) where (ξi)i≥0 is a 1-dimensional undelayed discrete renewal point process and (Ri)i≥0 is an i.i.d. sequence of N-valued random variables. At each site where ξi = 1 start an interval of length Ri . 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.

The whole paper is available here.



The Research, Innovation and Dissemination Center for Neuromathematics is hosted by the University of São Paulo and funded by FAPESP (São Paulo Research Foundation).


User login



1010 Matão Street - Cidade Universitária - São Paulo - SP - Brasil. 05508-090. See map.

55 11 3091-1717

General contact email:

Media inquiries email: