穆勒棘轮点击之间的亚稳态性
Metastability between the clicks of Muller's ratchet
AI总结：
本文证明了源自穆勒棘轮模型的三个随机过程拟平稳分布的存在唯一性，并在无限维不规则集合上建立了向拟平稳分布的全变差指数收敛，同时给出了收敛速度与突变经验分布的一致矩估计。
摘要：
我们证明了源自穆勒棘轮模型的三个随机过程的拟平稳分布的存在性与唯一性。该模型的发明旨在评估无性繁殖模式在仅依靠自然选择阻止有害突变积累方面的局限性。所考虑的主要模型是非经典的，因为它是一个随机扩散过程，在一个不规则的无限维集合上演化，并在一个超平面上具有硬杀伤（hard killing）。尽管如此，我们仍能证明在该情形下向拟平稳分布的全变差指数收敛。最后一个收敛结果中的参数与穆勒棘轮的核心参数直接相关。无论是对于无限维模型，还是对于具有大量但有限个潜在突变的近似模型，我们都推导出了向拟平稳分布收敛的速度。同样，我们给出了拟平稳状态下种群中突变经验分布的一致矩估计。
英文摘要：
We prove the existence and uniqueness of a quasi-stationary distribution for three stochastic processes derived from the model of Muller's ratchet. This model was invented with the aim of evaluating the limitations of an asexual reproduction mode in preventing the accumulation of deleterious mutations through natural selection alone. The main considered model is non-classical, as it is a stochastic diffusion evolving on an irregular set of infinite dimension with hard killing on an hyperplane. We are nonetheless able to prove exponential convergence in total variation to the quasi-stationary distribution even in this case. The parameters in this last convergence result are directly related to the core parameters of Muller's ratchet. The speed of convergence to the quasi-stationary distribution is deduced both for the infinite dimensional model and for approximations with a large yet finite number of potential mutations. Likewise, we give uniform moment estimates of the empirical distribution of mutations in the population under quasi-stationarity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
