Sum rules for effective resistances in infinite graphs

Greg Markowsky, José Luis Palacios

Research output: Contribution to journalArticleResearchpeer-review


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.

Original languageEnglish
Article number043403
Number of pages14
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number4
Publication statusPublished - 3 Apr 2017


  • stochastic processes

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