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
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.
|Additional Information:||© 2012 Cambridge University Press.|
|Library of Congress subject classification:||H Social Sciences > HA Statistics
Q Science > QA Mathematics
|Sets:||Departments > Mathematics|
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