Discrete One-Dimensional Coverage Process on a Renewal Process

Author(s)

Gallo, Sandro ^[1] ; Garcia, Nancy L. ^[2]

Affiliation

^[1] Univ Fed Sao Carlos, Dept Estat, Sao Carlos, SP - Brazil

^[2] Univ Estadual Campinas, Campinas, SP - Brazil

• Document type: Journal article
• Source: Journal of Statistical Physics; v. 173, n. 2, p. 381-397, OCT 2018.
• Web of Science Citations: 0

Abstract

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

• FAPESP's process: 14/26419-0 - Analysis of spatio-temporal aggregated data
• Grantee: Nancy Lopes Garcia
• Support type: Scholarships abroad - Research
• FAPESP's process: 17/07084-6 - Poincaré recurrence statistics and extreme value theory
• Grantee: Alexsandro Giacomo Grimbert Gallo
• Support type: Scholarships abroad - Research
• FAPESP's process: 15/09094-3 - Stochastic chains with long memory
• Grantee: Alexsandro Giacomo Grimbert Gallo
• Support type: Regular Research Grants
• FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
• Grantee: Jefferson Antonio Galves
• Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC