并行副本动力学的数学形式化
A mathematical formalization of the parallel replica dynamics
摘要：
本文的目的是为计算统计物理和分子动力学中的一个著名的数值方法，即由A.F.投票人。该方法的目的是有效地产生一个粗粒度的演变（状态到状态的动态）的一个给定的随机过程。该方法形式上包括同时考虑几个实现的随机过程，并跟踪实现，其中，最快，经历了一个重要的转变。使用所产生的动力学的特定属性，获得计算加速。在最好的情况下，这种加速接近所考虑的实现数量。通过与马尔可夫过程理论的联系，特别是利用准平稳分布的概念，我们提供了一个数学设置适当的理论评估的方法的性能，并可能改善它。
英文摘要：
The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the approach is to efficiently generate a coarse-grained evolution (in terms of state-to-state dynamics) of a given stochastic process. The approach formally consists in concurrently considering several realizations of the stochastic process, and tracking among the realizations that which, the soonest, undergoes an important transition. Using specific properties of the dynamics generated, a computational speed-up is obtained. In the best cases, this speed-up approaches the number of realizations considered. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it.
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。
