Strong law of large numbers on graphs and groups

Details Strong law of large numbers on graphs and groups Strong law of large numbers on graphs and groups

2009-04-06

arxiv.org/abs/0904.1005v2

Mathematics

Probability

29 pages, 2 figures, new references added, Introduction revised, Chernoff-like bound added

Scientific paper

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.

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