CONTACT PROCESSES ON RANDOM REGULAR GRAPHS

• 成果类型: Article
• 署名作者: Lalley, Steven; Su, Wei
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1249
• 发表日期: 2017
• 页码: 2061-2097
• 关键词: finite homogeneous trees; random-walks; TRANSITION; phase; set

摘要

We show that the contact process on a random d-regular graph initiated by a single infected vertex obeys the cutoff phenomenon in its supercritical phase. In particular, we prove that, when the infection rate is larger than the lower critical value of the contact process on the infinite d-regular tree, there are positive constants C, p depending on the infection rate such that for any epsilon > 0, when the number n of vertices is large then (a) at times t < (C - epsilon) log n the fraction of infected vertices is vanishingly small, but (b) at time (C + epsilon) log n the fraction of infected vertices is within epsilon of p, with probability p.