02/11/2022, 17:00 — 18:00 — Online
Ellen Saada, Université de Paris
Ergodicity of some dynamics of DNA sequences
In this joint work with M. Falconnet and N. Gantert, 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, introduced by Berard et al. in 2008, as well as three particular cases. 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.
