We study the absolute continuity and local limit theorems for homogeneous functionals defined on configurations of point processes (p.p.s). For empirical p.p.s, we show that under mild hypotheses the distribution of such a functional has a density. Moreover, we present results on convergence in total variation of this distribution to some limit.

中文翻译：

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点过程齐次泛函的绝对连续性和局部极限定理

我们研究了定义在点过程 (pps) 配置上的齐次泛函的绝对连续性和局部极限定理。对于经验 pps，我们表明在温和的假设下，这种泛函的分布具有密度。此外，我们展示了该分布的总变化收敛到一定限度的结果。