%0 Journal Article %1 tetali1991random %A Tetali, Prasad %D 1991 %I Kluwer Academic Publishers-Plenum Publishers %J Journal of Theoretical Probability %K effective_resistance electrical_networks random_walk random_walks_on_graphs resistance_distance return_time %N 1 %P 101-109 %R 10.1007/BF01046996 %T Random walks and the effective resistance of networks %U http://dx.doi.org/10.1007/BF01046996 %V 4 %X 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.

@article{tetali1991random, 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.}, added-at = {2014-04-02T06:20:24.000+0200}, author = {Tetali, Prasad}, biburl = {https://www.bibsonomy.org/bibtex/2c02b6958b861f2787b8241cd22e1dcb0/peter.ralph}, doi = {10.1007/BF01046996}, interhash = {5e5b88d3bab7808f49999a44561f62b8}, intrahash = {c02b6958b861f2787b8241cd22e1dcb0}, issn = {0894-9840}, journal = {Journal of Theoretical Probability}, keywords = {effective_resistance electrical_networks random_walk random_walks_on_graphs resistance_distance return_time}, language = {English}, number = 1, pages = {101-109}, publisher = {Kluwer Academic Publishers-Plenum Publishers}, timestamp = {2015-02-22T17:52:21.000+0100}, title = {Random walks and the effective resistance of networks}, url = {http://dx.doi.org/10.1007/BF01046996}, volume = 4, year = 1991 }