论文标题
非可逆包含过程的凝结和亚稳定行为
Condensation and Metastable Behavior of Non-reversible Inclusion Processes
论文作者
论文摘要
在本文中，我们对称为包容过程的相互作用粒子系统的亚稳态行为进行定量分析。对于包含过程，人们普遍认为，由于相互作用机理的吸引力，系统会核定颗粒的凝结。包含过程的亚稳定行为对应于在合适的时间尺度上凝结物的运动，相应的时间尺度的计算和凝结物运动的缩放限制的表征是纳入纳入过程的主要问题。以前，这些问题已解决用于[Bianchi，Dommers和Giardinà，Electronic of Poybility of Poybility of Poybility of Poybility of Electronic Journal，22：1-34，2017]中的可逆包含过程，本研究的主要贡献是将此分析扩展到广泛的非可逆包含过程。非可逆性是分析此类模型的主要障碍，这主要是因为对总体情况没有不变的度量的封闭式表达，而我们的主要成就是要克服这一困难。特别是，我们的结果表明，非可逆纳入过程的时间尺度和限制过程在定量和质量上与可逆性的过程分别不同。我们强调的是，据我们所知，这些结果是当不明确知道不变的度量时，这些结果是研究亚稳定性的第一个严格定量结果。此外，我们考虑了包含过程在大圆环上的亚稳态行为的热力学极限，如论文[Armendáriz，Grosskinsky和Loulakis，概率理论与相关领域，169：105-175，2017]。对于此模型，我们根据模型的不对称水平观察三个不同的时间尺度。
In this article, we perform quantitative analyses of metastable behavior of an interacting particle system known as the inclusion process. For inclusion processes, it is widely believed that the system nucleates the condensation of particles because of the attractive nature of the interaction mechanism. The metastable behavior of the inclusion processes corresponds to the movement of the condensate on a suitable time scale, and the computation of the corresponding time scale and the characterization of the scaling limit of the condensate motion are the main problems in the study of metastability of inclusion processes. Previously, these problems were solved for reversible inclusion processes in [Bianchi, Dommers, and Giardinà, Electronic Journal of Probability, 22: 1-34, 2017], and the main contribution of the present study is to extend this analysis to a wide class of non-reversible inclusion processes. Non-reversibility is a major obstacle to analyzing such models, mainly because there is no closed-form expression of the invariant measure for the general case, and our main achievement is to overcome this difficulty. In particular, our results demonstrate that the time scale and limiting process of non-reversible inclusion processes are quantitatively and qualitatively different from those of reversible ones, respectively. We emphasize that, to the best of our knowledge, these results are the first rigorous quantitative results in the study of metastability when the invariant measure is not explicitly known. In addition, we consider the thermodynamic limit of metastable behavior of inclusion processes on large torus as in the paper [Armendáriz, Grosskinsky, and Loulakis, Probability Theory and Related Fields, 169: 105-175, 2017]. For this model, we observe three different time scales according to the level of asymmetry of the model.
