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On a coloured tree with non i.i.d. random labels

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  • Michael, Skevi
  • Volkov, Stanislav

Abstract

We obtain new results for the probabilistic model introduced in Menshikov et al. (2007) and Volkov (2006) which involves a d-ary regular tree. All vertices are coloured in one of d distinct colours so that d children of each vertex all have different colours. Fix d2 strictly positive random variables. For any two connected vertices of the tree assign to the edge between them a label which has the same distribution as one of these random variables, such that the distribution is determined solely by the colours of its endpoints. A value of a vertex is defined as a product of all labels on the path connecting the vertex to the root. We study how the total number of vertices with value of at least x grows as x[downwards arrow]0, and apply the results to some other relevant models.

Suggested Citation

  • Michael, Skevi & Volkov, Stanislav, 2010. "On a coloured tree with non i.i.d. random labels," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1896-1903, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1896-1903
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    References listed on IDEAS

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    1. Volkov, Stanislav, 2006. "A probabilistic model for the 5x+1 problem and related maps," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 662-674, April.
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