Gabrielli Andrea
Statistical Mechanics and Complexity Center, INFM, Department of Physics, University La Sapienza of Rome, Piazzale Aldo Moro 2, 00185-Rome, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 2):066131. doi: 10.1103/PhysRevE.70.066131. Epub 2004 Dec 23.
The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. Particular attention is devoted to the kind of large-scale correlations that can be introduced by the displacement field and to the realizability of arbitrary "superhomogeneous" point processes.
分析了随机位移场对统计独立点过程的影响。随机位移场可分为两大类：空间相关和不相关。对于这两种情况，都找到了点过程的两点相关函数和功率谱的精确变换方程，并结合重要的典型例子对它们进行了详细研究。结果具有普遍性，适用于任何维度。特别关注了位移场可能引入的大规模相关性类型以及任意“超均匀”点过程的可实现性。
