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Article Dans Une Revue Markov Processes And Related Fields Année : 2020

Ergodicity of some dynamics of DNA sequences

Résumé

We define interacting particle systems on configurations of the integer lattice (with values in some finite alphabet) by the superimposition of two dynamics: a substitution process with finite range rates, and a circular permutation mechanism (called “cut-and-paste”) with possibly unbounded range. The model is motivated by the dynamics of DNA sequences: we consider an ergodic model for substitutions, the RN+YpR model ([BGP08]), with three particular cases, the models JC+cpg, T92+cpg, and RNc+YpR. We investigate whether they remain ergodic with the additional cut-and-paste mechanism, which models insertions and deletions of nucleotides. Using either duality or attractiveness techniques, we provide various sets of sufficient conditions, concerning only the substitution rates, for ergodicity of the superimposed process. They imply ergodicity of the models JC+cpg, T92+cpg as well as the attractive RNc+YpR, all with an additional cut-and-paste mechanism.
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Dates et versions

hal-02068161 , version 1 (14-03-2019)
hal-02068161 , version 2 (05-11-2019)
hal-02068161 , version 3 (10-03-2020)

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Mikael Falconnet, Nina Gantert, Ellen Saada. Ergodicity of some dynamics of DNA sequences. Markov Processes And Related Fields, 2020, Special Issue Dedicated to Guy Fayolle, on the Occasion of his 75th Birthday, 26 (4), pp.567-612. ⟨hal-02068161v3⟩
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