A simple proof of exponential decay of subcritical contact processes

• 成果类型: Article
• 署名作者: Swart, Jan M.
• 署名单位: Czech Academy of Sciences; Institute of Information Theory & Automation of the Czech Academy of Sciences
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0741-1
• 发表日期: 2018
• 页码: 1-9
• 关键词: phase-transition; percolation; sharpness

摘要

This paper gives a new, simple proof of the known fact that for contact processes on general lattices, in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity. The proof also yields an explicit bound on the survival probability below the critical recovery rate, which shows that the critical exponent associated with this function is bounded from below by its mean-field value. The main idea of the proof is that if the expected number of infected sites decays slower than exponentially, then this implies the existence of a harmonic function that can be used to show that the process survives for any lower value of the recovery rate.