Journal article

# ORDER-INVARIANT MEASURES ON CAUSAL SETS

Graham Brightwell, Malwina Luczak

ANNALS OF APPLIED PROBABILITY | INST MATHEMATICAL STATISTICS | Published : 2011

DOI: 10.1214/10-AAP736

#### Abstract

A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring together two different classes of random processes. In one class, we are given a fixed causal set, and we consider random natural extensions of this causal set: we think of the random enumeration as being generated one point at a time. In the other class of processes, we generate a random causal set, working from the bottom up, adding one new maximal element at each stage. Processes of both types can exhibit a property called order-invariance: if we stop the pro..

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#### Grants

#### Funding Acknowledgements

Supported in part by a grant from STICERD.