Exponential growth and continuous phase transitions for the contact process on trees
| Autor: | Xiangying Huang |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Phase transition Contact process Conjecture periodic trees Probability (math.PR) Lambda Critical value Galton-Watson trees Exponential growth 60K35 CMJ branching process FOS: Mathematics Tree (set theory) Statistics Probability and Uncertainty Mathematics - Probability Mathematics Branching process Mathematical physics |
| Zdroj: | Electron. J. Probab. |
| DOI: | 10.48550/arxiv.1911.03330 |
| Popis: | 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 $\lambda _{1}$ for weak survival, and the survival probability $p(\lambda )$ is continuous with respect to the infection rate $\lambda $. Applying this fact, we show the contact process on a general periodic tree experiences two phase transitions in the sense that $\lambda _{1} |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|