自旋翻转下的Widom-Rowlinson模型：准定域性的立即损失和急剧恢复
The Widom-Rowlinson model under spin flip: Immediate loss and sharp recovery of quasilocality
摘要：
我们考虑独立自旋翻转动力学下的连续Widom-Rowlinson模型，并研究时间演化的点过程是否以及何时具有（几乎）准局部规范（时间演化测度的吉布斯性质）.我们的研究首次分析了欧几里得空间中点粒子的吉布斯-非吉布斯跃迁。我们发现了一幅损失和恢复的图像，其中比晶格上随时间演化的自旋模型更快地失去了更多的规律性。我们表现出即时损失的准局部性的渗流制度，充分措施的不连续点的任何规格。对于颜色不对称的混合模型，存在从这种非a.s.准地方政权回到无处不在的吉布斯政权。在锐再入时间$t_G>0$，模型为a.s.拟局部的对于颜色对称模型，没有重入。在建设性的一面，对于所有的$t>t_G$，我们提供无处不在的时间演化措施的准局部规格，并给出精确的指数估计的边界条件的影响。
英文摘要：
We consider the continuum Widom-Rowlinson model under independent spin-flip dynamics and investigate whether and when the time-evolved point process has an (almost) quasilocal specification (Gibbs-property of the time-evolved measure). Our study provides a first analysis of a Gibbs-non-Gibbs transition for point particles in Euclidean space. We find a picture of loss and recovery, in which even more regularity is lost faster than it is for time-evolved spin models on lattices. We show immediate loss of quasilocality in the percolation regime, with full measure of discontinuity points for any specification. For the color-asymmetric percolating model, there is a transition from this non-a.s. quasilocal regime back to an everywhere Gibbsian regime. At the sharp reentrance time $t_G>0$ the model is a.s. quasilocal. For the color-symmetric model there is no reentrance. On the constructive side, for all $t>t_G$, we provide everywhere quasilocal specifications for the time-evolved measures and give precise exponential estimates on the influence of boundary conditions.
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