具有凝胶化的团簇凝聚模型的大偏差界
Large-deviation bounds for cluster coagulation models with gelation
浏览论文内容
中文总结 AI 辅助
该论文针对团簇凝聚模型，在局部紧致Polish空间上建立了路径wise大偏差界，涵盖凝胶化与非凝胶化情形，并给出了速率函数的凸对偶表示。
中文摘要 AI 辅助
我们在局部紧致Polish状态空间上，针对具有凝胶化核的团簇凝聚模型的经验测度流，建立了路径wise大偏差界。团簇凝聚过程是一个测度值马尔可夫跳跃过程，其中成对的团簇根据一个时间非齐次核$K(t,x,y,d z)$合并。增长足够快的核可能产生凝胶化：一种相变，其中质量在有限时间内从有限团簇群体中逃逸。我们首先证明经验流的紧性，并将每个子序列极限识别为时间非齐次多类型Flory方程的解，该方程通过一个守恒量解释凝胶化后的动力学。然后，我们在路径空间上建立一个具有变分速率函数的全局大偏差上界。我们还证明了在合适倾斜Flory方程的唯一解附近的局部下界。最后，我们给出了上速率函数的凸对偶表示，包括表示测度可能的奇异部分。我们的结果适用于具有连续质量函数的局部紧致Polish状态空间，在统一框架内涵盖了凝胶化和非凝胶化两种情形。
英文摘要
We establish pathwise large-deviation bounds for the empirical-measure flow of a cluster coagulation model with gelling kernels on a locally compact Polish state space. The cluster coagulation process is a measure-valued Markov jump process in which pairs of clusters merge according to a time-inhomogeneous kernel $K(t,x,y,d z)$. Kernels with sufficiently rapid growth may produce gelation: a phase transition in which mass escapes from the finite-cluster population in finite time. We first prove tightness of the empirical flows and identify every subsequential limit as a solution of the time-inhomogeneous multi-type Flory equation, which accounts for post-gelation dynamics through a conserved quantity. We then establish a global large-deviation upper bound on path space with a variational rate function. We also prove a local lower bound near paths that are unique solutions of suitable tilted Flory equations. Finally, we give a convex-dual representation of the upper rate function, including the possible singular part of the representing measure. Our results apply to locally compact Polish state spaces with continuous mass functions, encompassing both the gelling and non-gelling regimes within a unified framework.
发表机构
- School of Mathematical Sciences, University of Science and Technology of China（中国科学技术大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。
