We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances above a high threshold exists. Under the so-called anti-clustering condition, the extremal dependence is only local. Thus the index set can have a general form compared to previous literature [3, 21]. However, we cannot describe the clustering of extreme values in terms of the usual spectral tail measure [23] except for hyperrectangles or index sets in the lattice case. Using the recent extension of the spectral measure for star-shaped equipped space [18], the $\upsilon$-spectral tail measure provides a natural extension that describes the clustering effect in full generality.

翻译：我们考虑将固定的极端按固定的随机组合成一组,而不是任意增加的指数集。我们研究指数集的充足假设,这样就存在高于高阈值的超高的点随机字段的极限。在所谓的反集群条件下,极端依赖性只是局部的。因此,与以前的文献[3, 21]相比,指数集可以具有一般形式。然而,我们无法用通常的光谱尾量计量[23]来描述极端组合的[23],但拉蒂斯案的超矩形或指数集除外。利用最近对恒星形状设备空间的光谱测量[18],美元/超升元光谱尾量测量提供了一种自然延伸,全面概括地描述聚集效应。