Strong law of large numbers on graphs and groups

2009/04/06 by Natalia Mosina, Mosina, Natalia, Alexander Ushakov +1
Mathematics · #20P05 #60B99 #FOS: Mathematics #Group Theory (math.GR) #Probability (math.PR) #math.GR #math.PR #msc:20P05 #msc:60B99

paper · pdf · doi:10.48550/arxiv.0904.1005

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

arxiv created 2010/06/29 · arxiv updated 2010/07/01

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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