Coupling times with ambiguities for particle systems and applications to context-dependent DNA substitution models

TL;DR

This paper introduces a coupling time with ambiguities for interacting particle systems, providing tools to analyze ergodicity and convergence, with applications to DNA evolution models considering neighboring base influences.

Contribution

It develops a novel coupling framework for particle systems and applies it to complex DNA substitution models with context dependence.

Findings

Established conditions for ergodicity and convergence in perturbed systems

Applied coupling techniques to DNA evolution models with neighboring base effects

Provided bounds on mixing times and correlation decay

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 context-dependent 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.