Maxwell's coefficients are conditional probabilities
Author:
Reuben Hersh
Journal:
Proc. Amer. Math. Soc. 44 (1974), 449453
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.
 [1]
R. J. Griego and R. Hersh, Brownian motion and potential theory, Scientific American, March, 1969, pp. 6774.
 [2]
J. H. Jeans, Mathematical theory of electricity and magnetism, Cambridge Univ. Press, 1948, pp. 9297.
 [3]
John
Lamperti, Probability. A survey of the mathematical theory, W.
A. Benjamin, Inc., New YorkAmsterdam, 1966. MR 0206996
(34 #6812)
 [4]
J. R. Reitz and F. J. Milford, Foundations of electromagnetic theory, AddisonWesley, 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
(12,90a)
 [1]
 R. J. Griego and R. Hersh, Brownian motion and potential theory, Scientific American, March, 1969, pp. 6774.
 [2]
 J. H. Jeans, Mathematical theory of electricity and magnetism, Cambridge Univ. Press, 1948, pp. 9297.
 [3]
 J. Lamperti, Probability. A survey of the mathematical theory, Benjamin, New York, 1966, pp. 136139. MR 34 #6812. MR 0206996 (34:6812)
 [4]
 J. R. Reitz and F. J. Milford, Foundations of electromagnetic theory, AddisonWesley, Reading, Mass., 1960, p. 112.
 [5]
 M. Schiffer, Some recent developments in the theory of conformal mapping, appendix to R. Courant, Dirichlet's principle, conformal mapping and minimal surfaces, Interscience, New York, 1950. MR 0036317 (12:90a)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197403433796
PII:
S 00029939(1974)03433796
Keywords:
Maxwell's coefficients,
capacitance
Article copyright:
© Copyright 1974
American Mathematical Society
