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Proceedings of the American Mathematical Society

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Maxwell's coefficients are conditional probabilities


Author: Reuben Hersh
Journal: Proc. Amer. Math. Soc. 44 (1974), 449-453
MSC: Primary 60J65; Secondary 78.31
MathSciNet review: 0343379
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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.


References [Enhancements On Off] (What's this?)

  • [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