Mathematics – Probability
Scientific paper
Aug 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994ap%26ss.218..159v&link_type=abstract
Astrophysics and Space Science, vol. 218, no. 2, p. p. 159-174
Mathematics
Probability
8
Astronomical Models, Fractals, Functional Integration, Functionals, Galaxies, Gravitational Fields, Mass Distribution, Stellar Systems, Stochastic Processes, Variations, Correlation, Moments, Newton Theory, Probability Density Functions, Vector Analysis
Scientific paper
The stochastic gravitational fluctuations for a fractal mass distribution are analyzed by means of a functional integral approach. A general method is developed for evaluating the stochastic properties of vectorial additive random fields generated by a variable number of point sources obeying inhomogeneous Poisson statistics. A closed expression for the generating functional of the field is given in terms of the generating functional of the sources. The moments of the resulting vectorial field are finite if the correlation functions of the sources have short tails. In this case all cumulants of the field can be computed exactly: they are averages of the central moments of sources computed in terms of the probability density of the position of a source. The method is applied for analyzing the stochastic gravitational fluctuations generated by a fractal distribution of field sources (stars or galaxies). For a Newtonian force law the correlation functions of the sources are slowly decaying, the cumulants of the stochastic gravitational field are infinite and the probability density of the field intensity F is given by a Levy fractal stable law with a scaling exponent H depending on the fractal dimension df of the distribution of stars or galaxies: H = (df)/2.
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