Brightwell, Graham and Luczak, Malwina
(2009)
*Order-invariant measures on fixed causal sets.*
.
arXiv.

## Abstract

A causal set is a countably infinite poset in which every element is above finitely many others; causal sets are exactly the posets that have a linear extension with the order-type of the natural numbers -- we call such a linear extension a {\em natural extension}. We study probability measures on the set of natural extensions of a causal set, especially those measures having the property of {\em order-invariance}: if we condition on the set of the bottom k elements of the natural extension, each possible ordering among these k elements is equally likely. We give sufficient conditions for the existence and uniqueness of an order-invariant measure on the set of natural extensions of a causal set.

Item Type: | Monograph (Report) |
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Official URL: | http://arxiv.org/ |

Additional Information: | © 2009 The authors |

Divisions: | Mathematics |

Subjects: | Q Science > QA Mathematics H Social Sciences > HA Statistics |

Sets: | Departments > Mathematics |

Date Deposited: | 09 Apr 2010 13:59 |

Last Modified: | 19 Jan 2020 00:31 |

URI: | http://eprints.lse.ac.uk/id/eprint/27677 |

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