Strong law of large numbers on graphs and groups
Copyright policy )Strong law of large numbers on graphs and groups
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.
29 pages, 2 figures, new references added, Introduction revised, Chernoff-like bound added
- Stevens Institute of Technology United States
Distance in graphs, strong law of large numbers, 60B99, 20P05, Probability (math.PR), probabiliy measures on metric spaces, mean-sets of vertices, Group Theory (math.GR), Graphs and abstract algebra (groups, rings, fields, etc.), Chebyshev inequality, Chernoff bound, random vertices, free group, Probabilistic methods in group theory, FOS: Mathematics, Probability measures on groups or semigroups, Fourier transforms, factorization, Mathematics - Group Theory, Mathematics - Probability, configuration of mean-sets, shift search problem
Distance in graphs, strong law of large numbers, 60B99, 20P05, Probability (math.PR), probabiliy measures on metric spaces, mean-sets of vertices, Group Theory (math.GR), Graphs and abstract algebra (groups, rings, fields, etc.), Chebyshev inequality, Chernoff bound, random vertices, free group, Probabilistic methods in group theory, FOS: Mathematics, Probability measures on groups or semigroups, Fourier transforms, factorization, Mathematics - Group Theory, Mathematics - Probability, configuration of mean-sets, shift search problem
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