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Products of Stochastic Matrices and Averaging Dynamics

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Abstract

In this chapter, we introduce and review some of the results on products of stochastic matrices and averaging dynamics. Throughout this thesis, by a product of stochastic matrices, we mean left product of stochastic matrices. More precisely, let \(\{A(k)\}\) be a stochastic chain. By left product of stochastic matrices, we mean the product of the form \(A(k)\cdots A(t_0)\) where \(k\geq t_0\geq 0\) and k often approaches to infinity.

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References

  1. S. Chatterjee, E. Seneta, Towards consensus: Some convergence theorems on re–peated averaging. J. Appl. Probab. 14(1), 89–97 (1977)

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  3. R.A. Horn, C.R. Johnson, Matrix Analysis (Cambridge University Press, Cambridge, 1985)

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© 2012 Springer-Verlag Berlin Heidelberg

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Touri, B. (2012). Products of Stochastic Matrices and Averaging Dynamics. In: Product of Random Stochastic Matrices and Distributed Averaging. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28003-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-28003-0_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28002-3

  • Online ISBN: 978-3-642-28003-0

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