论文标题
在强烈的刚性超透射随机措施上
On strongly rigid hyperfluctuating random measures
论文作者
论文摘要
与以前的信念相反，我们提供了既有过度腐蚀又强烈刚性的固定恒星随机度量的例子。因此，我们研究由泊松超平面镶嵌顶点形成的超平面相交过程（臀部）。已知这些臀部是过度碰撞的，即有界观测窗口中点数的差异的差异要比窗口的大小快。在这里，我们表明臀部具有特别强大的刚性特性。对于任何有限的Borel套装$ B $，这是一个成倍小的（有限的）停止套件，足以重建$ B $中所有点的位置，实际上，所有超平面都与$ b $相交。因此，同样由任意（但固定）维度的超平面相互作用支持的随机度量也是超韧性的。我们的例子有助于寻找相关性，密度波动和刚性特性之间的关系。
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.
