Sum rules for effective resistances in infinite graphs
Probability
2017-04-26 v4
Abstract
Extending work of Foster, Doyle, and others, we show how the Foster Theorems, a family of results concerning effective resistances on finite graphs, can in certain cases be extended to infinite graphs. A family of sum rules is then obtained, which allows one to easily calculate the sum of the resistances over all paths of a given length. The results are illustrated with some of the most common grids in the plane, including the square, triangular, and hexagonal grids.
Keywords
Cite
@article{arxiv.1602.06002,
title = {Sum rules for effective resistances in infinite graphs},
author = {Greg Markowsky and José Luis Palacios},
journal= {arXiv preprint arXiv:1602.06002},
year = {2017}
}