A Quasispecies Continuous Contact Model in a Critical Regime

@article{Kondratiev2016AQC,
  title={A Quasispecies Continuous Contact Model in a Critical Regime},
  author={Yuri Kondratiev and Sergey A. Pirogov and Elena A. Zhizhina},
  journal={Journal of Statistical Physics},
  year={2016},
  volume={163},
  pages={357-373}
}
We study a new non-equilibrium dynamical model: a marked continuous contact model in d-dimensional space ($$d \ge 3$$d≥3). We prove that for certain values of rates (the critical regime) this system has the one-parameter family of invariant measures labelled by the spatial density of particles. Then we prove that the process starting from the marked Poisson measure converges to one of these invariant measures. In contrast with the continuous contact model studied earlier in Kondratiev (Infin… 

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