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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
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213262
Page Count: 9
You can always find the topics here!Topics: Ergodic theory, Matrices, Markov chains, Mathematical theorems, Perceptron convergence procedure, Mathematical sequences, Mathematical vectors, Probability distributions, Mathematical problems, Integers
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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.
Journal of Applied Probability © 1977 Applied Probability Trust