An improved upper bound for the critical value of the contact process on $\mathbb{Z} ^d$ with $d\geq 3$

Electronic Communications in Probability

Xiaofeng Xue¹ 

关键词: Contact process;    critical value;    upper bound;    linear system;   

DOI  :  10.1214/18-ECP177

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

By coupling the basic contact process with a linear system, we give an improved upper bound for the critical value $\lambda _c$ of the basic contact process on the lattice $\mathbb{Z} ^d$ with $d\geq 3$. As a direct corollary of our result, the critical value of the three-dimensional contact process is shown to be at most $0.34$.

【 授权许可】

CC BY