随机包装点过程的生成泛函：从硬核到载波检测
Generating Functionals of Random Packing Point Processes: From Hard-Core to Carrier Sensing
摘要：
本文研究了几种随机Packing过程的生成泛函：经典的Matérn硬核模型，它的扩展，$k$模型和随机序列Packing过程的一个例子$\infty$ -Matérn模型.我们首先给出了$\infty$ -Matérn模型是良好定义的一个充分条件（与其他两个模型不同，后者在无界空间上可能不是良好定义的）。然后给出了三种模型的点过程的母函数，作为一个微分方程的解。系列表示和边界上的生成功能的包装模型也推导出来。最后，我们从生成泛函出发，得到了所考虑的填充模型的矩测度和Palm分布。
英文摘要：
In this paper we study the generating functionals of several random packing processes: the classical Matérn hard-core model; its extensions, the $k$-Matérn models and the $\infty$-Matérn model, which is an example of random sequential packing process. We first give a sufficient condition for the $\infty$-Matérn model to be well-defined (unlike the other two, the latter may not be well-defined on unbounded spaces). Then the generating functional of the resulting point process is given for each of the three models as the solution of a differential equation. Series representations and bounds on the generating functional of the packing models are also derived. Last but not least, we obtain moment measures and Palm distributions of the considered packing models departing from their generating functionals.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
