Random Orderings and Unique Ergodicity of Automorphism Groups
Random Orderings and Unique Ergodicity of Automorphism Groups
复制标题
自同构群的随机排序和独特遍历性
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Lyons
中科院分区：
文献类型：
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作者：
Omer Angel;A. Kechris;R. Lyons
我们证明了有限图的唯一在同构和导出子图下不变的随机序是一致随机序。我们证明了这意味着随机图的自同构群的唯一遍历性。我们给出了其他结构的类似定理，例如，度量空间。在Glasner和Weiss关于整数的所有排列的群的例子之后，这些给出了唯一遍历群的第一个例子，除了紧群和极其从属的群。我们还将这些结果与某些特殊类型的图和度量空间的结果进行了比较，在这些图和度量空间中可以找到不一致的随机序。
We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner and Weiss’s example of the group of all permutations of the integers. We also contrast these results to those for certain special classes of graphs and metric spaces in which such random orderings can be found that are not uniform.