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• W2035811851 abstract "In this paper, we study randomized consensus processing over general random graphs. At time step k, each node will follow the standard consensus algorithm, or stick to current state by a simple Bernoulli trial with success probability p <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> . Connectivity-independent and arc-independent graphs are defined, respectively, to capture the fundamental independence of random graph processes with respect to a consensus convergence. Sufficient and/or necessary conditions are presented on the success probability sequence for the network to reach a global a.s. consensus under various conditions of the communication graphs. Particularly, for arc-independent graphs with simple self-confidence condition, we show that Σ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> p <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> = ∞ is a sharp threshold corresponding to a consensus 0 - 1 law, i.e., the consensus probability is 0 for almost all initial conditions if Σ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> p <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> converges, and jumps to 1 for all initial conditions if Σ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> p <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sub> diverges." @default.
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• W2035811851 date "2012-06-01" @default.
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• W2035811851 title "Agreeing under randomized network dynamics" @default.
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• W2035811851 doi "https://doi.org/10.1109/acc.2012.6315361" @default.
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