Table of Contents
Journal of Probability
Volume 2014 (2014), Article ID 852481, 6 pages
http://dx.doi.org/10.1155/2014/852481
Research Article

Hitting Times of Walks on Graphs through Voltages

1Electrical and Computer Engineering Department, The University of New Mexico, Albuquerque, NM 87131, USA
2Department of Computational Science and Statistics, Simón Bolívar University, Caracas 1080A, Venezuela

Received 6 January 2014; Accepted 25 April 2014; Published 20 May 2014

Academic Editor: Bernardo Coutinho dos Santos

Copyright © 2014 José Luis Palacios et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We derive formulas for the expected hitting times of general random walks on graphs, in terms of voltages, with very elementary electric means. Under this new light we revise bounds and hitting times for birth-and-death Markov chains and for walks on graphs with cutpoints, and give some exact computations on the necklace graph. We also prove Tetali’s formula for hitting times without making use of the reciprocity principle. In fact this principle follows as a corollary of our argument that also yields as corollaries the triangular inequality for effective resistances and the reversibility of the sum of hitting times around a tour.