### Abstract

We study collections of random variables characterized by independence requirements assigned for only a fraction of the joint values of the variables. Such classes of random variables generalize various known models, like one-dependent processes. We determine existence conditions, showing that existence is decidable, and then interpret such conditions in terms ofDutch Books.As an example, a newlow density based independence model is being developed, exhibiting a phase transition in the vacuum probability.

Original language | English (US) |
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Title of host publication | Mathematics Across Contemporary Sciences |

Editors | Taher Abualrub, Abdul Salam Jarrah, Sadok Kallel, Hana Sulieman, Sadok Kallel |

Publisher | Springer New York LLC |

Pages | 33-56 |

Number of pages | 24 |

ISBN (Print) | 9783319463094 |

DOIs | |

State | Published - 2017 |

Event | The 2nd International Conference on Mathematics and Statistics, AUS-ICMS 2015 - Sharjah, United Arab Emirates Duration: Apr 2 2015 → Apr 5 2015 |

### Publication series

Name | Springer Proceedings in Mathematics and Statistics |
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Volume | 190 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Other

Other | The 2nd International Conference on Mathematics and Statistics, AUS-ICMS 2015 |
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Country | United Arab Emirates |

City | Sharjah |

Period | 4/2/15 → 4/5/15 |

### Keywords

- Decidability
- Dutch book
- Existence conditions
- Independent random variables
- Partial independence

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Catalano, C., & Gandolfi, A. (2017). Partially independent random variables. In T. Abualrub, A. S. Jarrah, S. Kallel, H. Sulieman, & S. Kallel (Eds.),

*Mathematics Across Contemporary Sciences*(pp. 33-56). (Springer Proceedings in Mathematics and Statistics; Vol. 190). Springer New York LLC. https://doi.org/10.1007/978-3-319-46310-0_3