Exponential growth and continuous phase transitions for the contact process on trees

2019/11/08 by Xiangying Huang, Huang, Xiangying
Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1911.03330

openalex publication_date 2019/11/08 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

We study the supercritical contact process on Galton-Watson trees and periodic trees. We prove that if the contact process survives weakly then it dominates a supercritical Crump-Mode-Jagers branching process. Hence the number of infected sites grows exponentially fast. As a consequence we conclude that the contact process dies out at the critical value λ₁ for weak survival, and the survival probability p(λ) is continuous with respect to the infection rate λ. Applying this fact, we show the contact process on a general periodic tree experiences two phase transitions in the sense that λ₁

Citations

• Survival and extinction of epidemics on random graphs with general\n degrees

Related

• The Contact Process on Trees
• The contact process on the regular tree with random vertex weights
• The Contact Process on Periodic Trees
• The Contact Process on Random Graphs and Galton-Watson Trees
• The Contact Process on Periodic Trees