A probabilistic model for the 5k+1 problem and related maps
(2006) In Stochastic Processes and their Applications 116(4). p.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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4588133
- author
- Volkov, Stanislav LU
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Random environment on trees, Large deviations, First-passage percolation, 3x + 1 Problem
- in
- Stochastic Processes and their Applications
- volume
- 116
- issue
- 4
- pages
- 662 - 674
- publisher
- Elsevier
- ISSN
- 1879-209X
- language
- English
- LU publication?
- no
- id
- 055d8cf2-1c7e-4b0b-99fc-e784b7e68b91 (old id 4588133)
- alternative location
- http://www.sciencedirect.com/science/article/pii/S0304414905001602
- date added to LUP
- 2016-04-01 16:08:21
- date last changed
- 2020-06-09 14:06:55
@article{055d8cf2-1c7e-4b0b-99fc-e784b7e68b91, 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.}}, author = {{Volkov, Stanislav}}, issn = {{1879-209X}}, keywords = {{Random environment on trees; Large deviations; First-passage percolation; 3x + 1 Problem}}, language = {{eng}}, number = {{4}}, pages = {{662--674}}, publisher = {{Elsevier}}, series = {{Stochastic Processes and their Applications}}, title = {{A probabilistic model for the 5k+1 problem and related maps}}, url = {{https://lup.lub.lu.se/search/files/4580087/4588708.pdf}}, volume = {{116}}, year = {{2006}}, }