Author:
BRIGHTWELL GRAHAM,LUCZAK MALWINA
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 anatural extension. We study probability measures on the set of natural extensions of a causal set, especially those measures having the property oforder-invariance: if we condition on the set of the bottomkelements of the natural extension, each feasible ordering among thesekelements 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
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