We establish the Bahadur representation of sample quantiles for stabilizing score functionals in stochastic geometry and study local fluctuations of the corresponding empirical distribution function. The scores are obtained from a Poisson process. We apply the results to trimmed and Winsorized means of the score functionals and establish a law of the iterated logarithm for the sample quantiles of the scores.

翻译：我们在随机几何中建立了稳定得分泛函的样本分位数的Bahadur表示，并研究了相应经验分布函数的局部波动。这些得分来源于泊松过程。我们将结果应用于得分泛函的修剪均值与温索化均值，并建立了得分样本分位数的重对数律。