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A probabilistic model for the 5x+1 problem and related maps

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  • Volkov, Stanislav

Abstract

We construct a probabilistic model which "mimics" the behaviour of a certain number-theoretical algorithm. This model involves study of a binary tree with randomly labelled edges, such that the labels have different distributions, depending on their directions. A number of properties of this tree are rigorously studied. As an application, this study could suggest what one could expect in the original algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:4:p:662-674
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    Cited by:

    1. Doumas, Aristides V. & Papanicolaou, Vassilis G., 2016. "A randomized version of the Collatz 3x+1 problem," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 39-44.
    2. 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.

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