关于强刚性超涨落随机测度
On strongly rigid hyperfluctuating random measures
摘要：
与以前的信念相反，我们提供了平稳遍历随机措施的例子，这是超波动和强刚性。因此，我们研究由Poisson超平面镶嵌顶点构成的超平面交过程。已知这些HIP是超波动的，也就是说，有界观察窗口中的点的数量的方差比窗口的大小增长得更快。在这里，我们表明，HIP表现出特别强的刚性属性。对于任何有界博雷尔集$B$，指数小（有界）停止集足以重建$B$中所有点的位置，事实上，所有与$B$相交的超平面。因此，由任意（但固定）维度的超平面交点支持的随机测度也是超波动的。我们的例子有助于寻找相关性，密度波动和刚性属性之间的关系。
英文摘要：
In contrast to previous belief, we provide examples of stationary ergodic random measures that are both hyperfluctuating and strongly rigid. Therefore, we study hyperplane intersection processes (HIPs) that are formed by the vertices of Poisson hyperplane tessellations. These HIPs are known to be hyperfluctuating, that is, the variance of the number of points in a bounded observation window grows faster than the size of the window. Here we show that the HIPs exhibit a particularly strong rigidity property. For any bounded Borel set $B$, an exponentially small (bounded) stopping set suffices to reconstruct the position of all points in $B$ and, in fact, all hyperplanes intersecting $B$. Therefore, also the random measures supported by the hyperplane intersections of arbitrary (but fixed) dimension, are hyperfluctuating. Our examples aid the search for relations between correlations, density fluctuations, and rigidity properties.
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