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

S Volkov

doi:10.1016/j.spa.2005.11.007

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

S Volkov

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

5 Citations (Scopus)

Abstract

We construct a probabilistic model which â€œmimicsâ€� 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.

Translated title of the contribution	A probabilistic model for the 5x+1 problem and related maps
Original language	English
Pages (from-to)	662 - 674
Number of pages	13
Journal	Stochastic Processes and their Applications
Volume	116 (4)
DOIs	https://doi.org/10.1016/j.spa.2005.11.007
Publication status	Published - Apr 2006

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Publisher: Elsevier Ltd

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10.1016/j.spa.2005.11.007

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title = "A probabilistic model for the 5x+1 problem and related maps",

abstract = "We construct a probabilistic model which {\^a}€{\oe}mimics{\^a}€� 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.",

author = "S Volkov",

note = "Publisher: Elsevier Ltd",

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N1 - Publisher: Elsevier Ltd

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Y1 - 2006/4

N2 - We construct a probabilistic model which â€œmimicsâ€� 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.

AB - We construct a probabilistic model which â€œmimicsâ€� 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.

U2 - 10.1016/j.spa.2005.11.007

DO - 10.1016/j.spa.2005.11.007

M3 - Article (Academic Journal)

VL - 116 (4)

SP - 662

EP - 674

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

ER -

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

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