标题： 调制泊松-狄利克雷扩散，源于缓慢相的包含过程 显示英文标题

标题： Modulated Poisson-Dirichlet diffusions arising from inclusion processes with a slow phase

摘要： 我们研究带有额外慢相的平均场包含过程，在该慢相中，粒子相互作用以与系统大小倒数成比例的消失速率发生。 在热力学极限下，这些系统在高粒子密度下表现出凝聚，形成尺寸发散的簇。 我们的主要结果提供了包含过程对一种新型两组分无限维随机扩散的法律收敛，描述了固态凝聚相和微观流体相的共同演化。 特别是，我们建立了两个相之间的非平凡质量交换。 所得的标度极限扩展了泊松-狄利克雷扩散（Ethier 和 Kurtz，1981），引入了一个额外的控制过程来调节其参数。 我们的结果基于生成器差异的经典估计，在这种情况下产生非消失的确定性误差界限。 我们通过显示瞬时凝聚来提供缺失的概率要素，其中粒子簇立即集中在消失的体积分数上。 我们进一步在紧致状态空间上一般地建立了极限动力学的适定性，作为 Feller 过程。 显示英文摘要

摘要： We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high particle density, forming clusters of diverging size. Our main result provides convergence in law of inclusion processes to a novel two-component infinite-dimensional stochastic diffusion, describing the co-evolution of the solid condensed and microscopic fluid phase. In particular, we establish non-trivial mass exchange between the two phases. The resulting scaling limit extends the Poisson-Dirichlet diffusion (Ethier and Kurtz, 1981), introducing an additional control process that modulates its parameters. Our result builds on classical estimates of generator differences, which in this setting yield non-vanishing deterministic error bounds. We provide the missing probabilistic ingredient by showing instantaneous condensation, with particle clusters concentrating on a vanishing volume fraction immediately. We further establish the well-posedness of the limiting dynamics generally as Feller processes on a compact state space.