Random walks and the effective resistance of networks
Journal of Theoretical Probability, 4 (1):
101-109 (1991)DOI: 10.1007/BF01046996
Abstract
In this article we present an interpretation of effective resistance in electrical
networks in terms of random walks on underlying graphs. Using this charac-
terization we provide simple and elegant proofs for some known results in ran-
dom walks and electrical networks. We also interpret the Reciprocity theorem
of electrical networks in terms of traversals in random walks. The byproducts
are (a) precise version of the triangle inequality for effective resistances, and (b)
an exact formula for the expected one-way transit time between vertices.
