Brightwell, Graham and Luczak, Malwina J.
(2012)
*Order-invariant measures on fixed causal sets.*
Combinatorics, Probability and Computing, 21 (03).
pp. 330-357.
ISSN 0963-5483

## 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 natural extension. We study probability measures on the set of natural extensions of a causal set, especially those measures having the property of order-invariance: if we condition on the set of the bottom k elements of the natural extension, each feasible 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: | Article |
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Official URL: | http://journals.cambridge.org/action/displayJourna... |

Additional Information: | © 2012 Cambridge University Press. |

Divisions: | Mathematics |

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

Sets: | Departments > Mathematics |

Date Deposited: | 04 May 2012 08:51 |

Last Modified: | 20 Feb 2019 18:29 |

URI: | http://eprints.lse.ac.uk/id/eprint/43397 |

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