Moscow Mathematical Journal

Volume 19, Issue 1, January–March 2019 pp. 121–132.

A Quasispecies Continuous Contact Model in a Subcritical Regime

Authors: Sergey Pirogov (1) and Elena Zhizhina (1)
Author institution:(1) Institute for Information Transmission Problems, Russian Academy of Sciences

Summary:

We study a non-equilibrium dynamical model: a marked continuous contact model in d-dimensional space, d>1. In contrast with the continuous contact model in a critical regime, see previous work by Kondratiev, Kutoviy, Pirogov, and Zhizhina, the model under consideration is in the subcritical regime and it contains an additional spontaneous spatially homogeneous birth from an external source. We prove that this system has an invariant measure. We prove also that the process starting from any initial distribution converges to this invariant measure.

2010 Math. Subj. Class. 60K35, 60J75, 60J80, 82C21, 82C22.

Keywords: Continuous contact model, marked configurations, correlation functions, statistical dynamics.

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