Sum rules for effective resistances in infinite graphs

Greg Markowsky; José Luis Palacios

doi:10.1088/1742-5468/aa6503

Sum rules for effective resistances in infinite graphs

Greg Markowsky, José Luis Palacios

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

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.

Original language	English
Article number	043403
Number of pages	14
Journal	Journal of Statistical Mechanics: Theory and Experiment
Volume	2017
Issue number	4
DOIs	https://doi.org/10.1088/1742-5468/aa6503
Publication status	Published - 3 Apr 2017

Keywords

stochastic processes

Access to Document

10.1088/1742-5468/aa6503

Cite this

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title = "Sum rules for effective resistances in infinite graphs",

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.",

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AU - Palacios, José Luis

PY - 2017/4/3

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N2 - 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.

AB - 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.

KW - stochastic processes

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DO - 10.1088/1742-5468/aa6503

M3 - Article

AN - SCOPUS:85018252846

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JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

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ER -

Sum rules for effective resistances in infinite graphs

Abstract

Keywords

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Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this

Sum rules for effective resistances in infinite graphs

Abstract

Keywords

Access to Document

Other files and links

Projects

Planar Brownian motion and complex analysis

New Stochastic Processes with Applications in Finance

Cite this