Random walks and the effective resistance of networks
type: Item
instance of: scholarly article
title: Random walks and the effective resistance of networks
zbMATH Open document ID: 0722.60070
DOI: 10.1007/BF01046996
author: Prasad Tetali
published in: Journal of Theoretical Probability
publication date: 1991-01-01T00:00:00Z
review text: A simple network is a finite electrical network comprised only of unit resistances. Identifying the network with a graph \(G=(V,E)\), a random walk on G is defined as a stochastic process on V in which a transition from x, independently of the past, leads to each of the d(x) (the degree) neighbors of x with probability 1/d(x). A random walk from x to y begins at the former and terminates when it first enters the latter. It is shown that the effective resistance \(R_{xy}\) between nodes x and y is equal to the expected number of traversals along any specific edge (x,z) by a random walk from x to y. Several consequences of this result are discussed, including the reciprocity theorem for networks.
reviewed by: Alan F. Karr
Mathematics Subject Classification ID: 60G50
Mathematics Subject Classification ID: 60K10
zbMATH DE Number: 4190857
zbMATH Keywords: electrical network
zbMATH Keywords: random walk
zbMATH Keywords: reciprocity theorem for networks
MaRDI profile type: Publication
cites work: The electrical resistance of a graph captures its commute and cover times
cites work: Q3706275
cites work: Random walks on graphs
cites work: Q5528211
full work available at URL: https://doi.org/10.1007/bf01046996
OpenAlex ID: W1986269714
description: scientific article; zbMATH DE number 4190857