Contact process under renewals II

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Fontes, Luiz Renato¹  Mountford, Thomas S.²  Vares, Maria Eulalia³ 

[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo, SP, Brazil

[2] Ecole Polytech Fed Lausanne, Dept Math, CH-1015 Lausanne, Switzerland

[3] Univ Fed Rio de Janeiro, Inst Matemat, Rio De Janeiro, RJ, Brazil

关键词: Contact process;    Percolation;    Renewal process;   

DOI  :  10.1016/j.spa.2019.04.008

来源: Elsevier

【 摘 要 】

We continue the study of renewal contact processes initiated in a companion paper, where we showed that if the tail of the interarrival distribution mu is heavier than t(-alpha) for some alpha < 1 (plus auxiliary regularity conditions) then the critical value vanishes. In this paper we show that if mu has decreasing hazard rate and tail bounded by t(-alpha) with alpha > 1, then the critical value is positive in the one-dimensional case. A more robust and much simpler argument shows that the critical value is positive in any dimension whenever the interarrival distribution has a finite second moment. (C) 2019 Published by Elsevier B.V.

【 授权许可】

Free