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Scattering Analysis of Point Processes and Random Measures
Author(s) -
Hanisch K.H.
Publication year - 1984
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211170119
Subject(s) - mathematics , point process , scattering , intensity (physics) , distribution (mathematics) , function (biology) , statistical physics , distribution function , mathematical analysis , statistics , physics , quantum mechanics , evolutionary biology , biology
In the present paper scattering analysis of point processes and random measures is studied. Known formulae which connect the scattering intensity with the pair distribution function of the studied structures are proved in a rigorous manner with tools of the theory of point processes and random measures. For some special fibre processes the scattering intensity is computed. For a class of random measures, namely for “grain‐germ‐models”, a new formula is proved which yield the pair distribution function of the “grain‐germ‐model” in terms of the pair distribution function of the underlying point process (the “germs”) and of the mean structure factor and the mean squared structure factor of the particles (the “grains”).