Ergodic Properties of Randomly Coloured Point Sets
Ergodic Properties of Randomly Coloured Point Sets
复制标题
随机着色点集的遍历性质
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
C. Richard
中科院分区：
文献类型：
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作者：
P. Müller;C. Richard
摘要本文给出了一个研究局部紧二次可数空间中可度量化么模群连续正确作用的随机着色点集的框架。首先，我们构造和描述一个适当的动力系统一致离散无色点集。对于有限的局部复杂性的点集，我们几何遍历模式频率的特征。一般的框架允许我们将一个随机着色的点集。我们得到了有限范围依赖的随机着色点集的遍历定理。特别注意排除特殊情况下，唯一遍历系统。该设置允许一个简单的应用程序，以随机着色的图形
Abstract We provide a framework for studying randomly coloured point sets in a locally compact second-countable space on which a metrizable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical system for uniformly discrete uncoloured point sets. For point sets of finite local complexity, we characterize ergodicity geometrically in terms of pattern frequencies. The general framework allows us to incorporate a random colouring of the point sets. We derive an ergodic theorem for randomly coloured point sets with finite-range dependencies. Special attention is paid to the exclusion of exceptional instances for uniquely ergodic systems. The setup allows for a straightforward application to randomly coloured graphs