Coupling times with ambiguities for particle systems and applications to contextdependent DNA substitution models
Abstract
We define a notion of coupling time with ambiguities for interacting particle systems, and show how this can be used to prove ergodicity and to bound the convergence time to equilibrium and the decay of correlations at equilibrium. A motivation is to provide simple conditions which ensure that perturbed particle systems share some properties of the underlying unperturbed system. We apply these results to contextdependent substitution models recently introduced by molecular biologists as descriptions of DNA evolution processes. These models take into account the influence of the neighboring bases on the substitution probabilities at a site of the DNA sequence, as opposed to most usual substitution models which assume that sites evolve independently of each other.
 Publication:

arXiv eprints
 Pub Date:
 December 2007
 arXiv:
 arXiv:0712.0072
 Bibcode:
 2007arXiv0712.0072B
 Keywords:

 Mathematics  Probability;
 Quantitative Biology  Quantitative Methods;
 60J25;
 60K35;
 92D20
 EPrint:
 33 pages