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arXiv · 1309.0158

Robustness of large-scale stochastic matrices to localized perturbations

Giacomo Como·Fabio Fagnani
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Abstract

Upper bounds are derived on the total variation distance between the invariant distributions of two stochastic matrices differing on a subset W of rows. Such bounds depend on three parameters: the mixing time and the minimal expected hitting time on W for the Markov chain associated to one of the matrices; and the escape time from W for the Markov chain associated to the other matrix. These results, obtained through coupling techniques, prove particularly useful in scenarios where W is a small subset of the state space, even if the difference between the two matrices is not small in any norm. Several applications to large-scale network problems are discussed, including robustness of Google's PageRank algorithm, distributed averaging and consensus algorithms, and interacting particle systems.

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Giacomo Como, Fabio Fagnani. 2015-05-16. Robustness of large-scale stochastic matrices to localized perturbations. https://arxiv.org/abs/1309.0158

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