Strong law of large numbers on graphs and groups

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Mosina, Natalia
Ushakov, Alexander
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Abstract
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We consider (graph-)group-valued random element $\xi$, discuss the properties of a mean-set $\ME(\xi)$, and prove the generalization of the strong law of large numbers for graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev's inequality for $\xi$ and Chernoff-like asymptotic bounds. In addition, we prove several results about configurations of mean-sets in graphs and discuss computational problems together with methods of computing mean-sets in practice and propose an algorithm for such computation.
Comment: 29 pages, 2 figures, new references added, Introduction revised, Chernoff-like bound added
Keywords
Mathematics - Probability, Mathematics - Group Theory, 60B99, 20P05
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