Abstract
In Chap. 3, we showed that regardless of the structure and any assumption on a random chain we have \(i{\leftrightarrow} _Wj\subseteq \Uptheta_{ij}\) for any \(i,j\in [m]\) where \(\Uptheta_{ij}\) is the event that i, j belong to the same connected component of the infinite flow graph of \({\{W(k)\}}.\)
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Notes
- 1.
We refer to \(\|\cdot\|_\pi\) as a semi-norm because in general \(\|x\|_{\pi}=0\) does not imply \(x=0,\) unless \(\pi>0\) in which case \(\|\cdot\|_{\pi}\) is a norm.
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Touri, B. (2012). Infinite Flow Stability. In: Product of Random Stochastic Matrices and Distributed Averaging. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28003-0_4
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