Abstract
HOLTSMARK1, in an electrostatic context, and Chandrasekhar2, in the case of a Newtonian gravitational field, have given a simple model which describes the electrostatic or gravitational field at an arbitrary point in space. They take the point as the origin of coordinates and calculate the field there due to point charges or masses which are scattered randomly and homogeneously throughout the space. Specifically, the field is where K is a proportionality constant, and in a sphere of radius R it is supposed that there are N points scattered randomly and located at t1, …, tN. By letting N and R→∞ in such a way that the density of points 3N/4πR3→λ, Holtsmark showed that the probability distribution of XR(0) converges to a limit, being the distribution of XP(0), say.
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References
Holtsmark, J., Ann. Phys., 58, 577 (1919).
Chandrasekhar, S., Rev. Mod. Phys., 15, 1, chapter 4 (1943).
Camm, G. L., Mon. Not. Roy. Astron. Soc., 126, 283 (1963).
Freud, P. G. O., Meheshwari, A. M., and Schönberg, E., Astrophys. J., 157, 857 (1969).
Daley, D. J., J. Appl. Probability, 8, No. 1 (1971).
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DALEY, D. The Non-existence of Stationary Infinite Newtonian Universes and a Multi-dimensional Model of Shot Noise. Nature 227, 935 (1970). https://doi.org/10.1038/227935a0
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DOI: https://doi.org/10.1038/227935a0
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