Journal
PHYSICAL REVIEW E
Volume 70, Issue 6, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.70.066131
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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.
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