# 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…

## 17 Citations

### A Quasispecies Continuous Contact Model in a Critical Regime

- MathematicsJournal of Statistical Physics
- 2016

We study a new non-equilibrium dynamical model: a marked continuous contact model in d-dimensional space (d≥3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

### General contact processes: inhomogeneous models, models on graphs and on manifolds

- Mathematics
- 2021

The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the…

### Invariant measures for spatial contact model in small dimensions

- Mathematics
- 2018

We study invariant measures of continuous contact model in small dimensional spaces ($d =1,2$). Under general conditions we prove that in the critical regime this system has the one-parameter set of…

### Fecundity regulation in a spatial birth-and-death process

- MathematicsStochastics and Dynamics
- 2020

We study a Markov birth-and-death process on a space of locally finite configurations, which describes an ecological model with a density-dependent fecundity regulation mechanism. We establish…

### Long-Time Behavior for Subcritical Measure-Valued Branching Processes with Immigration

- MathematicsPotential Analysis
- 2022

In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial…

### Contact processes on general spaces. Models on graphs and on manifolds

- MathematicsElectronic Journal of Probability
- 2022

The contact process is a particular case of birth-and-death processes on inﬁnite particle conﬁgurations. We consider the contact processes on locally compact separable metric spaces. We prove the…

### Periodic Homogenization of Nonlocal Operators with a Convolution-Type Kernel

- MathematicsSIAM J. Math. Anal.
- 2017

In the topology of resolvent convergence the family of rescaled operators converges to a second order elliptic operator with constant coefficients, and it is shown that for the related family of Markov processes the invariance principle holds.

### Open quasispecies systems: New approach to evolutionary adaptation

- BiologyChinese Journal of Physics
- 2021

### Mathematical On the spectrum of convolution operator with a potential

- Mathematics
- 2022

This paper focuses on the spectral properties of a bounded self-adjoint operator in L 2 ( R d ) being the sum of a convolution operator with an integrable convolution kernel and an operator of…

### On spectra of convolution operators with potentials

- Mathematics
- 2022

. This paper focuses on the spectral properties of a bounded self-adjoint operator in L 2 ( R d ) being the sum of a convolution operator with an integrable convolution kernel and an operator of…

## References

SHOWING 1-10 OF 11 REFERENCES

### Nonequilibrium Glauber-type dynamics in continuum

- Mathematics
- 2006

We construct the nonequilibrium Glauber dynamics as a Markov process in configuration space for an infinite particle system in continuum with a general class of initial distributions. This class we…

### CORRELATION FUNCTIONS AND INVARIANT MEASURES IN CONTINUOUS CONTACT MODEL

- Mathematics
- 2008

We study the continuous version of the contact model. Using an analytic approach, we construct the non-equilibrium contact process as a Markov process on configuration space. The construction is…

### ON CONTACT PROCESSES IN CONTINUUM

- Mathematics
- 2006

We introduce a continuous version of the contact model which is well known and widely studied in the lattice case. Under certain general assumptions on the infection spreading characteristics, we…

### The hypercycle. A principle of natural self-organization. Part A: Emergence of the hypercycle.

- BiologyDie Naturwissenschaften
- 1977

An analysis of experimental data regarding RNA and D N A replication reveals that a sufficient amount of information for the build up of a translation machinery can be gained only via integration of several different replicative units (or reproductive cycles) throughfimctional linkages.

### HARMONIC ANALYSIS ON CONFIGURATION SPACE I: GENERAL THEORY

- Mathematics
- 2002

We develop a combinatorial version of harmonic analysis on configuration spaces over Riemannian manifolds. Our constructions are based on the use of a lifting operator which can be considered as a…

### A principle of natural self-organization

- BiologyNaturwissenschaften
- 2004

An analysis of experimental data regarding RNA and DNA replication at various levels of organization reveals, that a sufficient amount of information for the build up of a translation machinery can be gained only via integration of several different replicative units (or reproductive cycles) through functional linkages.

### What is a quasispecies?

- BiologyCurrent topics in microbiology and immunology
- 2006

The quasispecies concept has been shown to affect the pathway of evolution and has been studied on RNA viruses which have a particularly high mutation rate.

### Statistical Mechanics:

- PhysicsNature
- 1937

AbstractPROF. R. H. FOWLER'S monumental work on statistical mechanics has, in this the second edition, in his own modest words, been rearranged and brought more up to date. But the new volume is much…