Mathematics – Probability
Scientific paper
Nov 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991a%26a...251..385c&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 251, no. 2, Nov. 1991, p. 385-388.
Mathematics
Probability
3
Cosmology, Statistical Correlation, Probability Density Functions, Statistical Distributions
Scientific paper
The definition of the correlation function is not unique and depends on the choice of the normalization constraint. Such a lack of uniqueness strongly influences the correlation amplitude and, as a consequence, may change the interpretation of physical quantities in the system considered. This effect occurs in systems where it is not possible to define a mean value for the probability distribution of the average densities (e.g. an infinite fractal), while in the opposite case (as, for instance, liquids, where the average density is well defined, since it does not depend on the sample geometry) there is no contradiction between the different definitions of the correlation function. In this paper, the sample dependence of the amplitudes of the different correlation functions is indicated in sets where the mean density of the statistical population is unknown or cannot be defined.
Calzetti Daniela
Giavalisco Mauro
Ruffini Remo
Wiedenmann Gerda
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