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Abstract
We consider (graph-)group-valued random element ξ, discuss the properties of a mean-set 𝔼(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.
Keywords.: Probability measures on graphs and groups; average; expectation; mean-set; strong law of large numbers; Chebyshev inequality; Chernoff bound; configuration of mean-sets; free group; shift search problem
Received: 2010-12-22
Published Online: 2011-02-03
Published in Print: 2011-May
© de Gruyter 2011