一类广义镶嵌随机场
A general class of mosaic random fields
摘要：
我们提出了一个拓扑空间$M$上的随机场模型，它统一了众所周知的模型，如泊松超平面细分模型，随机令牌模型和枯叶模型。除了将这些子模型从$\mathbb{R}^d$推广到其他空间，如$d$维单位球$\mathbb{S}^d$，我们的构造还扩展了经典模型本身，例如，通过用任意离散分布代替泊松分布。此外，构造方法直接产生精确和快速的模拟过程。通过研究一般模型的协方差结构，我们恢复了$\mathbb{R}^d$和$\mathbb{S}^d$上的各种显式相关函数，并得到了几个新的相关函数。
英文摘要：
We present a model of a random field on a topological space $M$ that unifies well-known models such as the Poisson hyperplane tessellation model, the random token model, and the dead leaves model. In addition to generalizing these submodels from $\mathbb{R}^d$ to other spaces such as the $d$-dimensional unit sphere $\mathbb{S}^d$, our construction also extends the classical models themselves, e.g. by replacing the Poisson distribution by an arbitrary discrete distribution. Moreover, the method of construction directly produces an exact and fast simulation procedure. By investigating the covariance structure of the general model we recover various explicit correlation functions on $\mathbb{R}^d$ and $\mathbb{S}^d$ and obtain several new ones.
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。
