Order-invariant measures on fixed causal sets

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

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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 (Other) http://arxiv.org/ © 2009 The authors Q Science > QA MathematicsH Social Sciences > HA Statistics Departments > Mathematics 09 Apr 2010 13:59 http://eprints.lse.ac.uk/27677/