Ergodic properties of randomly coloured point sets

Details Ergodic properties of randomly coloured point sets Ergodic properties of randomly coloured point sets

2010-05-26

arxiv.org/abs/1005.4884v3

Mathematics

Dynamical Systems

52 pages. Reference [AMN] added, together with corresponding changes. Accepted for publication in the Canadian Journal of Math

Scientific paper

We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical system for uniformly discrete uncoloured point sets. For point sets of finite local complexity, we characterise ergodicity geometrically in terms of pattern frequencies. The general framework allows to incorporate a random colouring of the point sets. We derive an ergodic theorem for randomly coloured point sets with finite-range dependencies. Special attention is paid to the exclusion of exceptional instances for uniquely ergodic systems. The setup allows for a straightforward application to randomly coloured graphs.

Affiliated with

Also associated with

No associations

Rating

Ergodic properties of randomly coloured point 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 Ergodic properties of randomly coloured point sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ergodic properties of randomly coloured point sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-606734