Mathematics – Probability
Scientific paper
2009-01-02
Annals of Applied Probability 2011, Vol. 21, No. 4, 1493-1536
Mathematics
Probability
Published in at http://dx.doi.org/10.1214/10-AAP736 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst
Scientific paper
10.1214/10-AAP736
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 process after some fixed number of steps, then, conditioned on the structure of the causal set, every possible order of generation of its elements is equally likely. We develop a framework for the study of order-invariance which includes both types of example: order-invariance is then a property of probability measures on a certain space. Our main result is a description of the extremal order-invariant measures.
Brightwell Graham
Luczak Malwina
No associations
LandOfFree
Order-invariant measures on causal sets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Order-invariant measures on causal sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Order-invariant measures on causal sets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380900