The Mutating Contact Process: Model Introduction and Qualitative Analysis of Phase Transitions in its Survival

2018/01/04 by Idan Alter, Alter, Idan, Gideon Amir +1
Mathematics · Physics and Astronomy · #60K35 #82C22 #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.1801.01530

openalex publication_date 2018/01/04 · openalex created_date 2018/01/12 · openalex updated_date 2026/07/28

Abstract

We introduce and study the mutating contact process, a variant of the multitype contact process, where one type mutates at a constant rate to the other type. We prove that on ℤ a single mutant cannot survive while on \mathbbT_d there are distinct weak survival and extinction of a single mutant phases, yet the limiting distribution concentrates on configurations with no mutants of the first type for any values of the parameters.

Related

• The asymmetric multitype contact process
• Multitype Contact Process on \Z: Extinction and Interface
• Two-scale multitype contact process: coexistence in spatially explicit metapopulations
• Phase transition for a non-attractive infection process in heterogeneous environment
• Renewal Contact Processes: phase transition and survival