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Towards consensus: some convergence theorems on repeated averaging

Published online by Cambridge University Press:  14 July 2016

S. Chatterjee  and
E. Seneta
S. Chatterjee
Affiliation:
New York University
E. Seneta
Affiliation:
Australian National University
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Abstract

The problem of tendency to consensus in an information-exchanging operation is connected with the ergodicity problem for backwards products of stochastic matrices. For such products, weak and strong ergodicity, defined analogously to these concepts for forward products of inhomogeneous Markov chain theory, are shown (in contrast to that theory) to be equivalent. Conditions for ergodicity are derived and their relation to the consensus problem is considered.

Keywords

CONSENSUSREPEATED AVERAGINGSTOCHASTIC MATRICESBACKWARDS PRODUCTSERGODICITYINHOMOGENEOUS MARKOV CHAINS
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 1 , March 1977 , pp. 89 - 97
Copyright
Copyright © Applied Probability Trust 1977 

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