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Journal Article

Towards Consensus: Some Convergence Theorems on Repeated Averaging

S. Chatterjee and E. Seneta
Journal of Applied Probability
Vol. 14, No. 1 (Mar., 1977), pp. 89-97
DOI: 10.2307/3213262
Stable URL: http://www.jstor.org/stable/3213262
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Towards Consensus: Some Convergence Theorems on Repeated Averaging
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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.

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