Maxwell's coefficients are conditional probabilities

Author:
Reuben Hersh

Journal:
Proc. Amer. Math. Soc. **44** (1974), 449-453

MSC:
Primary 60J65; Secondary 78.31

DOI:
https://doi.org/10.1090/S0002-9939-1974-0343379-6

MathSciNet review:
0343379

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Abstract | References | Similar Articles | Additional Information

Abstract: The capacitance coefficients of electrostatics are represented as conditional probabilities associated with Brownian motion. It follows, as an immediate consequence, that these coefficients depend monotonically on their domains.

**[1]**R. J. Griego and R. Hersh,*Brownian motion and potential theory*, Scientific American, March, 1969, pp. 67-74.**[2]**J. H. Jeans,*Mathematical theory of electricity and magnetism*, Cambridge Univ. Press, 1948, pp. 92-97.**[3]**John Lamperti,*Probability. A survey of the mathematical theory*, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR**0206996****[4]**J. R. Reitz and F. J. Milford,*Foundations of electromagnetic theory*, Addison-Wesley, Reading, Mass., 1960, p. 112.**[5]**R. Courant,*Dirichlet’s Principle, Conformal Mapping, and Minimal Surfaces*, Interscience Publishers, Inc., New York, N.Y., 1950. Appendix by M. Schiffer. MR**0036317**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0343379-6

Keywords:
Maxwell's coefficients,
capacitance

Article copyright:
© Copyright 1974
American Mathematical Society