Point processes and stochastic displacement fields

Details Point processes and stochastic displacement fields Point processes and stochastic displacement fields

2004-09-22

arxiv.org/abs/cond-mat/0409594v1

Phys.Rev.E70:066131,2004

Physics

Condensed Matter

Statistical Mechanics

17 pages, 7 figures

Scientific paper

10.1103/PhysRevE.70.066131

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. A 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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