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arXiv · 0904.1005

Strong law of large numbers on graphs and groups

Natalia Mosina·Alexander Ushakov
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Abstract

We consider (graph-)group-valued random element $ξ$, discuss the properties of a mean-set $\ME(ξ)$, 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 $ξ$ 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.

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Natalia Mosina, Alexander Ushakov. 2010-06-29. Strong law of large numbers on graphs and groups. https://arxiv.org/abs/0904.1005

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