Corpus ID: 115169803

Stochastic Models for the 3x+1 and 5x+1 Problems

@article{Kontorovich2009StochasticMF,
  title={Stochastic Models for the 3x+1 and 5x+1 Problems},
  author={Alex Kontorovich and J. Lagarias},
  journal={arXiv: Number Theory},
  year={2009}
}
This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are rigorously analyzable, and yield heuristic predictions (conjectures) for the behavior of 3x+1 orbits and 5x+1 orbits. 
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