Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A random walk related to the capacitance of the circular plate condenser


Author: E. Reich
Journal: Quart. Appl. Math. 11 (1953), 341-345
MSC: Primary 65.0X
DOI: https://doi.org/10.1090/qam/57625
MathSciNet review: 57625
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the solution of Love's equation for the capacitance of the circular plate condenser can be expressed in terms of the mean duration of a certain one-dimensional random walk with absorbing barriers. The interpretation as a random walk makes it possible to confirm the fact that the actual capacitance of the condenser is always larger than the value given by the standard approximation for small separations, and yields an upper bound as well. In addition to its theoretical interest, the random walk appears to provide a practical means for the calculation of the capacitance by a Monte Carlo technique.


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

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  • [2] Mark Kac and Harry Pollard, The distribution of the maximum of partial sums of independent random variables, Canadian J. Math. 2 (1950), 375–384. MR 0036465
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DOI: https://doi.org/10.1090/qam/57625
Article copyright: © Copyright 1953 American Mathematical Society


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