论文标题
可逆纳入过程的亚竞争力的第二个时间尺度
Second Time Scale of the Metastability of Reversible Inclusion Processes
论文作者
论文摘要
我们研究了[Bianchi，Dommers和Giardinà，Electronic of Poberitional of Poberitional of Poberapity of Election journal of Electronic Journal，22：1-34，2017]，研究可逆包含过程的亚稳态行为的第二个时间尺度，该研究提出了同一模型的第一个时间尺度，并推测了多个时间尺度的方案。我们表明，$ n/d_ {n}^{2} $确实是最通用的可逆包含过程的正确的第二个时间尺度，因此证明了前有关研究的第一个猜想。在这里，$ n $表示粒子的数量，而$ d_ {n} $表示系统的随机性较小。这项研究的主要障碍是在计算能力的尖锐渐近物质方面出现的，并且由于粒子构型的复杂几何形状，在前研究中使用的方法并不直接适用。为了克服这些问题，我们首先彻底检查过渡速率的景观，以获得平衡电位的适当测试功能，这为容量提供了上限。然后，我们修改诱导的测试流，并精确地估计亚稳态山谷附近的平衡电位，以获得能力的正确下限。
We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by [Bianchi, Dommers, and Giardinà, Electronic Journal of Probability, 22: 1-34, 2017], which presented the first time scale of the same model and conjectured the scheme of multiple time scales. We show that $N/d_{N}^{2}$ is indeed the correct second time scale for the most general class of reversible inclusion processes, and thus prove the first conjecture of the foresaid study. Here, $N$ denotes the number of particles, and $d_{N}$ denotes the small scale of randomness of the system. The main obstacles of this research arise in calculating the sharp asymptotics for the capacities, and in the fact that the methods employed in the former study are not directly applicable due to the complex geometry of particle configurations. To overcome these problems, we first thoroughly examine the landscape of the transition rates to obtain a proper test function of the equilibrium potential, which provides the upper bound for the capacities. Then, we modify the induced test flow and precisely estimate the equilibrium potential near the metastable valleys to obtain the correct lower bound for the capacities.
