连续统中离散时间排斥型过程的度量性质
Metric properties of discrete time exclusion type processes in continuum
摘要：
引入并研究了一类新的具有同步更新的连续统排斥型过程。遍历平均的粒子速度和它们的连接到其他统计量，特别是粒子密度（所谓的基本图）进行了严格的分析。主要的技术工具是以非标准方式应用的“动态”耦合：我们不证明成功耦合的存在（甚至可能不成立），而是将其存在/不存在作为重要的诊断工具。尽管这种方法不能直接应用于格系统，它允许获得新的结果的格系统嵌入到系统的连续。交通流建模的应用进行了讨论。
英文摘要：
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to the particle density (the so called Fundamental Diagram) is analyzed rigorously. The main technical tool is a "dynamical" coupling applied in a nonstandard fashion: we do not prove the existence of the successful coupling (which even might not hold) but instead use its presence/absence as an important diagnostic tool. Despite that this approach cannot be applied to lattice systems directly, it allows to obtain new results for the lattice systems embedding them to the systems in continuum. Applications to the traffic flows modelling are discussed as well.
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