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

Stanislav Volkov

Stochastic Processes and their Applications, 2006, vol. 116, issue 4, 662-674

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.

Keywords: Random; environment; on; trees; Large; deviations; First-passage; percolation; 3x+1; Problem (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (2)

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