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Order-invariant measures on fixed causal sets

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

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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 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
Official URL: http://journals.cambridge.org/action/displayJourna...
Additional Information: © 2012 Cambridge University Press.
Library of Congress subject classification: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 04 May 2012 08:51
URL: http://eprints.lse.ac.uk/43397/

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