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Licensed Unlicensed Requires Authentication Published by De Gruyter February 3, 2011

Strong law of large numbers on graphs and groups

  • Natalia Mosina EMAIL logo and Alexander Ushakov

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.

Received: 2010-12-22
Published Online: 2011-02-03
Published in Print: 2011-May

© de Gruyter 2011

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