论文标题
随机讲述是I.I.D的因素
Random interlacement is a factor of i.i.d
论文作者
论文摘要
随机讲述点过程（由sznitman引入，由Teixeira推广）是一个泊松点过程，该过程是在瞬态图$ g $上标记为doubly Infinite Infinite最近的邻居轨迹模型时移的空间。我们表明，任何瞬态及物图$ g $上的随机介学点过程是I.I.D.的一个因素，即可以从I.I.D的家族中构造。随机变量通过图表的顶点索引，通过可测量的映射。我们的证明使用软局部时间方法的变体（由Popov和Teixeira介绍）来构建插入点过程，这是模型的有限长度变体的几乎确定的限制，随着长度的增加。我们还讨论了一种更直接的方法，以证明插入点过程是I.I.D的一个因素。当$ g $不占据时，哪个是有效的。
The random interlacement point process (introduced by Sznitman, generalized by Teixeira) is a Poisson point process on the space of labeled doubly infinite nearest neighbour trajectories modulo time-shift on a transient graph $G$. We show that the random interlacement point process on any transient transitive graph $G$ is a factor of i.i.d., i.e., it can be constructed from a family of i.i.d. random variables indexed by vertices of the graph via an equivariant measurable map. Our proof uses a variant of the soft local time method (introduced by Popov and Teixeira) to construct the interlacement point process as the almost sure limit of a sequence of finite-length variants of the model with increasing length. We also discuss a more direct method of proving that the interlacement point process is a factor of i.i.d. which works if and only if $G$ is non-unimodular.
