粒子系统的耦合时间及其在上下文相关DNA替代模型中的应用
Coupling times with ambiguities for particle systems and applications to context-dependent DNA substitution models
摘要：
我们定义了一个概念的耦合时间与相互作用的粒子系统的模糊性，并展示了如何可以用来证明遍历性和约束的收敛时间的平衡和衰减的相关性在平衡。一个动机是提供简单的条件，以确保受扰粒子系统共享一些基本的未受扰系统的属性。我们将这些结果应用于最近由分子生物学家引入的上下文相关的替代模型，作为DNA进化过程的描述。这些模型考虑了相邻碱基对DNA序列某个位点的取代概率的影响，而不是大多数通常的取代模型，这些模型假设位点相互独立地进化。
英文摘要：
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.
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