Point processes and stochastic displacement fields.
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.
Gabrielli
Andrea
A
Statistical Mechanics and Complexity Center, INFM, Department of Physics, University La Sapienza of Rome, Piazzale Aldo Moro 2, 00185-Rome, Italy.