THE CONTACT PROCESS ON DYNAMIC REGULAR GRAPHS: SUBCRITICAL PHASE AND MONOTONICITY

• 成果类型: Article
• 署名作者: Schapira, Bruno; Valesin, Daniel
• 署名单位: Aix-Marseille Universite; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/24-AOP1721
• 发表日期: 2025
• 页码: 753-796
• 关键词: exponential extinction time; metastability

摘要

We study the contact process on a dynamic random d-regular graph with an edge-switching mechanism as well as an interacting particle system that arises from the local description of this process called the herds process. Both these processes were introduced in (da Silva, Oliveira and Valesin (2021)); there it was shown that the herds process has a phase transition with respect to the infectivity parameter lambda, depending on the parameter v that governs the edge dynamics. Improving on a result of (da Silva, Oliveira and Valesin (2021)), we prove that the critical value of lambda is strictly decreasing with v. We also prove that, in the subcritical regime, the extinction time of the herds process started from a single individual has an exponential tail. Finally, we apply these results to study the subcritical regime of the contact process on the dynamic d-regular graph. We show that, starting from all vertices infected, the infection goes extinct in a time that is logarithmic in the number of vertices of the graph, with high probability.