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Order-Invariant Measures on Fixed Causal Sets

Published online by Cambridge University Press:  19 January 2012

GRAHAM BRIGHTWELL  and
MALWINA LUCZAK
GRAHAM BRIGHTWELL
Affiliation:
Department of Mathematics, London School of Economics and Political Science, Houghton Street, London WC2A 2AE, UK (e-mail: g.r.brightwell@lse.ac.uk)
MALWINA LUCZAK
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK (e-mail: m.luczak@sheffield.ac.uk)
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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.

Keywords

Primary 06A0760C05
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 3 , May 2012 , pp. 330 - 357
Copyright
Copyright © Cambridge University Press 2012

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